TOPOGRAPHIC 

STADIA  SURVEYING 


A  MANUAL  WITH  REDUCTION  TABLES 

ANrf 

A  NEW  TYPE  OF  REDUCTION  DIAGRAM 


BY 

C.  E.  GRUNSKY,  ENG.D. 

^ 

MEM.  AM.  Soc.  C.E. 


18  ILLUSTRATIONS 
and  A  FOLDING  PLATE 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

25  PARK  PLACE 

1917 


COPYRIGHT,  1917,  BY 
C.  E.  GRUNSKY 


PREFACE 


THE  notes  on  Stadia  Surveying,  presented  in  this  manual, 
were  assembled  a  number  of  years  ago.  For  the  benefit 
of  the  surveyor  who  has  occasion  to  use  the  telemeter  they 
are  now  made  available  in  printed  form.  The  method  of 
surveying  herein  described  and  the  special  type  of  diagram 
for  the  reduction  of  stadia  notes,  herewith  supplied,  have 
been  found  so  satisfactory  by  the  author,  and  by  others 
who  have  tried  them  out,  that  he  considers  it  a  duty  to  give 
the  profession  the  benefit  of  his  experience. 

C.  E.  GRUNSKY. 

SAN  FRANCISCO,  CAL., 
June  1,  1917. 


370008 


CONTENTS 


STADIA  SURVEYING 

HAPTER  PAGE 

I.  Introduction  and  Definitions 1 

Theoretical  Considerations 3 

The  Porro  Telescope 5 

II.  The  Stadia  Formula 9 

Derivation  of  Formula 9 

Determination  of  the  Rating  Factor 10 

General  Formulas  for  Inclined  Sights 12 

Approximation  Formulas 16 

Suggestions  Relating  to  the  Use  of  the  Formulas  17 

III.  Diagrams  for  the  Reduction  of  Stadia  Measure- 

ments. , 19 

Diagrammatic  Solution  of  the  Stadia  Formulas  19 

The  Diagram  Furnished  with  this  Manual 22 

IV.  The  Slide-rule  as  an  Aid  in  Reducing  Stadia  Notes  24 

Modification  of  Formulas  for  Slide-rule  Work . .  24 

V.  Methods  of  Stadia  Surveying 26 

Stadia  Surveys  without  the  Use  of  the  Magnetic 

Needle 26 

Stadia  Surveys  with  the  Use  of  the  Magnetic 

Needle 28 

VI.  Practical  Suggestions 30 

Departures  from  Ordinary  Practice 30 

The  Stadia  Rod 30 

The  Elimination  of  the  Height  of  the  Telescope 

above  the  Instrument  Station  Plug 35 

The  Liberal  Use  of  the  Magnetic  Needle 37 

v 


vi  CONTENTS 


Stadia  Notes 38 

Note-book  Sample  Pages 40 

Vertical  Angles  Measured  with  an  Alidade 44 

The  Amount  of  Error  when  the  Sighting  Point 

does  not  Bisect  the  Intercept 44 

Table  1.     Corrections  for  too  Large  a  Ver- 

cal  angle 45 

Table  2.  Corrections  for  too  Small  a  Ver- 
tical angle 46 

The  Amount  of  Error  Due  to  Inclined  Rod 47 

The  Accuracy  of  Telemeter  Surveys 48 

Table  3.  Corrections  for  Departures  cf  the 
Stadia  Rod  from  a  True  Vertical  Posi- 
tion, etc 49 

Table  4.  Corrections  for  Departure  of  the 
Stadia  Rod  From  a  True  Vertical  Posi- 
tion, etc 50 

The  Effect  of  Refraction ' 51 

VII.  The  Platting  of  Stadia  Notes 52 

VIII.  Tables: 

Table  5.     Values  of  e  cos  a  and  e  sin  a 54 

Table  6.     Stadia  Reduction  Table '    57 

Table  7.  U.  S.  Geological  Survey  Tables  for 

Obtaining  Differences  in  Elevation 63 

Conversion  of  Feet  into  Miles 91 

IX.  How  to  Use  the  Stadia  Diagram 93 

INDEX 97 

STADIA  DIAGRAM  IN  COVER  POCKET 


TOPOGRAPHIC  STADIA  SURVEYING 


CHAPTER  I 
INTRODUCTION  AND  DEFINITIONS 

Telescope     Cross-hairs,    Adjustable     or    Fixed.    The 

telescope  to  be  used  in  stadia  work  is  equipped  with  three 
horizontal  cross-hairs.  The  spacing  of  these  cross-hairs 
may  be  either  adjustable  or  fixed.  For  general  use  the  fixed 
cross-hairs  are  preferred  by  most  engineers  and  surveyors, 
though  they  are  not  without  their  disadvantages. 

When  the  cross-hairs  are  adjustable  frequent  testing  of 
the  instrument  rating  may  be  necessary. 

When  the  cross-hairs  are  fixed  (this  term  being  here  use  in 
the  sense  of  permanent  in  their  relative  positions,  i.e.,  non- 
adjustable),  the  instrument's  rating  as  reported  by  its 
maker  should  be  carefully  tested  before  any  surveys  requiring 
the  limit  of  attainable  accuracy  are  undertaken. 

Tachymetry.  Tachymetry  is  that  branch  of  surveying 
which  deals  with  the  rapid  measurement  of  distances,  as,  for 
instance,  the  determination  of  distance  from  an  instrument 
by  sighting  with  its  telescope  to  a  rod. 

Telemeter.  The  term  "  telemeter "  may  be  applied  to 
any  telescope  equipped  with  cross-hairs  for  measuring  dis- 
tance, or  equipped  with  micrometer  screw  or  other  device 
for  accurate  determination  of  the  length  of  rod  subtended 
by  an  angle  of  known  amplitude.  (Only  the  instruments 
equipped  with  cross-hairs  are  taken  into  consideration  in 


2  TOPOGRAPHIC  STADIA  SURVEYING 

this  discussion,  as  these  alone  have  come  into  general  use  in 
topographic  surveying). 

Stadia-rod  or  Telemeter-rod  or  "  The  Rod."  These  designa- 
tions are  applied  to  the  rod  which  is  used  in  connection  with  a 
telemeter  for  measuring  distance.  The  rod  may  be  equipped 
with  targets,  or,  as  is  more  common,  it  may  be  a  self-reading 
rod;  that  is  to  say,  a  rod  on  whose  face  the  subdivisions 
and  repetitions  of  the  distance  unit  are  so  plainly  indicated  by 
markings  and  figures  that  the  instrument-man  can  read  the  rod 
without  recourse  to  targets.  The  use  of  a  target-rod  is  a  refine- 
ment not  justified  by  the  accuracy  attainable  with  a  telemeter 
and  need  not,  therefore,  receive  any  special  consideration. 

Intercept.  The  intercept  is  the  length  of  that  portion  of 
the  rod,  in  stadia  units,  appearing  between  two  cross-hairs, 
generally  between  the  lower  and  the  upper  hairs. 

The  Anallatic  Point.  The  anallatic  point  of  any  instru- 
ment is  that  point  from  which  the  distance  to  a  rod  which  is 
read  for  distance  is  proportional  to  the  intercept.  For  an 
ordinary  telescope  the  anallatic  point  lies  a  principal  focal 
length  in  front  of  the  object  glass. 

The  Telemeter  Constant.  This  is  a  value  to  be  deter- 
mined for  each  telemeter.  It  is,  for  an  ordinary  telescope, 
the  sum  of  the  principal  focal  distance  of  the  object-glass 
plus  the  length  of  the  part  of  the  telescope  from  the 
instrument's  vertical  axis  to  the  object-glass.  It  is  the  dis- 
tance (measured  along  the  collimation  axis  of  the  telescope) 
of  the  anallatic  point  from  the  vertical  axis  of  the  instrument. 

The  Rod-reading.  The  rod-reading,  as  this  expression  is 
used  in  this  manual,  is  one  hundred  times  the  intercept. 
Unless  otherwise  noted  it  is  to  be  understood  that  an  instru- 
ment rating  of  100  is  assumed.  In  other  words  one  stadia 
unit  on  the  rod  is  to  be  read  and  entered  in  the  notes  as  100. 

The  Sighting  Point.  The  sighting  point  on  the  rod  is  that 
point  on  the  rod  to  which  the  sight  is  taken  for  vertical  angles. 
It  is  the  point  on  the  rod  on  which  the  middle  cross-hair  is 
set  for  the  vertical  angle. 


TOPOGRAPHIC   STADIA  SURVEYING  3 

The  Rating  Factor.  The  rating  factor  of  any  instrument  is 
that  factor  by  which,  when  sighting  horizontally  to  a  vertical 
rod,  the  intercept  (read  in  any  linear  unit  as  for  example  in 
feet),  must  be  multiplied  to  find  the  distance  to  the  rod 
(in  the  same  linear  unit),  from  the  anallatic  point. 

The  Principal  Focal  Distance.  The  expression  "  principal 
focal  distance  "  is  the  distance  from  a  lens  at  which  parallel 
rays  of  light  passing  through  it  are  brought  to  a  focus. 

The  Stadia  Unit.  The  stadia  unit  is  a  rod  increment  of 
such  length  that  one  such  unit  will  be  intercepted,  when 
sighting  horizontally,  for  each  100  or  200  or  other  number 
of  units  (depending  on  the  rating  factor  of  the  instrument), 
that  the  rod  is  distant  from  the  anallatic  point. 

Theoretical    Considerations.     The    object-glass    of    the 


ordinary  telescope  of  a  transit  or  plane-table  alidade  is  a 
convex  lens.     For  every  convex  lens: 


Here  B  is  the  distance  from  the  lens  to  some  object  whose 
image  appears  on  the  opposite  side  of  the  lens  at  the  distance 
b,  and  /  is  the  principal  focal  distance  of  the  lens. 

A  horizontal  sight  being  assumed,  let  S,  Fig.  2,  represent 
the  intercept  on  a  rod  and  s  the  actual  space  between 
the  cross-hairs.  Then 

&=*     .....  .    .     .     .     (2) 


4  TOPOGRAPHIC  STADIA  SURVEYING 

Combining  (1)  and  (2) 


(3) 


FIG.  2. 

The  value  of  s  and  the  value  of  /  for  any  telescope  are  con- 
stant, therefore,  -  is  a  constant, 
s 

Make 


Then 


B-f=KS. 


(4) 


The  distance  B-f,  Fig.  3,  is  proportional  to  the  inter- 
cept S. 

The  relation  between  B  —  /,  S,  s  and  /  expressed  in  Eq.  (3) 
appears  also  from  the  optical  principle  illustrated  in  Fig.  3. 


TOPOGRAPHIC   STADIA  SURVEYING  5 

The  Porro  Telescope.  It  is  practicable  to  construct  a 
telescope  in  which  the  anallatic  point  will  coincide  with  the 
vertical  axis  of  the  instrument.  This  fact  was  first  demon- 
strated by  an  Italian  officer,  Mr.  Porro,  who,  in  1823,  con- 


structed and  described  a  telescope  in  which  lenses  were  so 
combined  that  all  rod-readings  were  proportional  to  the  dis- 
tances from  the  center  of  the  instrument.  How  this  was 
done  will  appear  by  reference  to  Fig.  4.  The  object-glass  0 
and  the  auxiliary  lens  0'  are  so  placed  that  the  vertical  axis 


L . :  i-  z> 


of  the  instrument,  at  C,  is  between  them.  The  object-glass 
0  has  a  longer  focal  distance  than  that  of  the  ordinary  tele- 
scope. If  the  construction  is  such  that  the  points  C  and  F' 
are  conjugate  foci  for  the  lens  0  and  the  two  lenses  are  rigidly 
connected,  the  angle  at  C  will  be  constant.  In  other 
words,  the  intercept  S  will  be  proportional  to  the  distance  D, 


6  TOPOGRAPHIC  STADIA   SURVEYING 

Referring  to  this  type  of  instrument,  which  has  not  come 
into  use  in  this  country,  Mr.  A.  Lietz  says:* 

"  Since  stadia  measurements  originate  from  the  outer  focus  of 
the  objective  lens,  and  not  from  the  center  of  the  instrument,  it 
becomes  somewhat  troublesome  to  apply  a  correction  therefor  on 
inclined  sights,  for,  since  the  corrections  remain  constant  for  any 
distance  and  vary  with  the  angle  of  inclination  only,  it  is  not 
practical  to  incorporate  them  directly  into  the  tabular  values  em- 
ployed in  reducing  stadia  observations.  Such  tables  are  usually 
augmented  by  placing  the  corrections  due  to  what  is  generally  termed 
the  constant  e  at  the  bottom  thereof.  To  overcome  this  difficulty, 
and  to  make  every  reading  date  directly  from  the  center  of  the 
instrument,  the  Italian  Porro  invented  a  method  in  1823,  which  is 
now  beginning  to  be  better  known.  This  method  has  been  fre- 
quently discussed.  The  Journal  of  the  Franklin  Institute  contains 
an  article  in  a  number  as  far  back  as  1868.  The  Engineering  News 
of  November  8,  1890,  has  a  short  discussion  by  one  of  our  best 
writers  on  these  subjects,  Prof.  J.  B.  Johnson,  of  Washington  Uni- 
versity, St.  Louis. 

"  A  convex  lens  of  required  focal  length  is  inserted  between  the 
objective  and  the  eyepiece,  which  transfers  the  anallatic  point  to 
the  occupied  center.  Theoretically  this  is  necessary,  for  the  observed 
vertical  angles  have  their  common  vertex  in  the  center  of  the  arc, 
or  horizontal  axis  of  the  telescope;  while  the  vertex  of  the  dias- 
timometric  angle  lies  outside  of  the  objective,  a  distance  of  14  ins. 
from  the  center  of  the  instrument  in  the  ordinary  large  .transit. 
This  would  cause  slight  errors  in  vertical  angle  and  distance,  which 
disappear  in  the  Porro  telescope. 

"  There  are  very  substantial  reasons,  however,  why  this  anallatic 
lens  has  not  found  a  more  general  application  in  modern  surveying 
instruments,  for  it  is  not  a  new  thing  with  which  we  are  dealing,  but 
a  principle  that  was  known  and  used  over  half  a  century  ago;  and 
these  reasons  will  now  be  briefly  considered. 

"  By  inserting  an  additional  lens  the  equivalent  focal  length  of 
the  objective  is  considerably  decreased,  and  the  power  and  capacity 
are  thereby  correspondingly  lessened.  To  exemplify  this,  reference 
is  made  to  an  actual  test  of  which  the  results  were  accessible  to  me. 
In  this  case  the  focal  length  of  the  objective  equaled  13 \  ins.,  that  of 
the  inserted  lens  5  ins.  and  the  distance  between  them  9f  ins.  The 
equivalent  focal  length  of  the  combination  was,  therefore,  7f  ins. 
The  image  of  the  system  lay  2j  ins.  behind  the  anallatic  lens,  and 
its  distance  from  the  objective,  therefore,  11  f  ins.  Here  we  notice 
*  Journal  Assoc.  Engrg.  Socs.,  Vol.  19,  1897,  p.  256  et  seq. 


TOPOGRAPHIC   STADIA  SURVEYING  7 

that  the  available  focal  length  has  been  shortened  by  the  lens  com- 
bination 4|  ins.,  which  is  a  direct  loss  of  nearly  37%.  An  ordinary 
telescope  with  a  focus  of  11  f  ins.,  possessing  an  eyepiece  with  one  of 
5  in.,  would  have  a  power  of  23,  while  the  Porro  telescope  under  sim- 
ilar conditions  shows  only  15,  indicating  the  same  percentage  of  loss 
in  power.  There  is,  however,  a  slight  gain  in  brightness  with  the 
same  aperture  of  objectives,  for  the  reason  that  the  admitted  light 
is  concentrated  in  a  smaller  space.  In  order  to  make  up  for  the  loss 
in  power,  due  to  the  anallatic  lens,  a  more  powerful  eyepiece  must  be 
made  use  of.  One  with  an  equivalent  focal  length  of  T<-  in.  would 
about  compensate  the  37%  loss,  but  the  brightness  of  the  image 
would  not  then  be  quite  up  to  that  of  the  ordinary  telescope,  since 
the  middle  lens  will  cause  a  slight  loss  of  light  by  reason  of  reflection 
and  absorption.  This,  however,  might  again  be  rectified  by  giving 
the  objective  a  somewhat  larger  aperture. 

"  While  it  is  readily  seen  that  a  Porro  telescope  might  be  con- 
structed fully  up  to  the  capacity  of  our  ordinary  transit  telescope, 
it  is  also  apparent  that  much  greater  care  and  refinement  would 
have  to  be  resorted  to  to  reach  it,  for  it  is  very  important  that  the 
entire  mechanical  work  should  be  perfectly  in  harmony  with  the 
greater  optical  requirements.  The  tubes  must  be  absolutely  straight, 
the  axes  of  the  lenses  must  be  identical  and  their  principal  planes 
normal  thereto.  Greater  care  must  be  exercised  in  the  construction 
of  the  objective,  it  being  necessary  to  correct  therein  for  the  aberra- 
tion due  to  sphericity  and  achromatism  of  the  anallatic — which  is 
usually  a  simple  convex  lens — if  we  would  retain  a  clear  and  dis- 
tinct image. 

"It  is  a  problem  for  the  instrument  maker  to  construct  the  Porro 
telescope  so  that  there  shall  be  no  complicated  parts,  and  no  excess 
of  cost  to  speak  against  it.  The  additional  lens,  whose  focal  distance 
depends  upon  the  length  of  the  telescope  and  the  location  of  the 
center  of  the  instrument,  is  placed  in  front  of  and  not  too  far  from 
the  cross-hair  diaphragm.  Its  distance  from  the  objective  must 
necessarily  remain  constant,  and  any  motion  of  the  latter  in  the  tube 
must  be  made  with  the  middle  lens  also.  The  lenses  must  move 
together. 

"It  might  be  a  more  advantageous  construction  to  adopt  the  mov- 
able eyepiece,  and  to  focus  by  shifting  the  cross-hair  diaphragm  in 
connection  therewith. 

"This  lens  combination  has  one  peculiar  advantage  that  must  not 
be  left  unmentioned,  which  is  that  it  requires  but  a  very  small  tele- 
scopic slide  movement  to  focus  from  long  to  short  distances  and  vice 
versa.  A  range  of  half  an  inch  may  be  sufficient  to  cover  all  the 
required  lengths  of  sight. 


8  TOPOGRAPHIC   STADIA  SURVEYING 

"In  building  the  tube,  provision  must  also  be  made  for  readily 
removing  the  inner  lens  in  order  to  clean  it,  which  would  probably 
be  frequently  required.  The  arrangements  for  this  purpose  must  be 
so  contrived  that  the  lens  may  be  replaced  in  its  proper  position  and 
accurately  adjusted  to  the  required  optical  conditions. 

"Every  feature  goes  to  show  that  the  mechanical  work  of  such  a 
telescope  must  be  of  the  highest  order,  if  it  shall  meet  the  demands 
made  upon  it.  With  the  cheaper  grade  of  surveying  instruments  a 
Porro  telescope  is  an  impossibility. 

"Granted  that  we  have  a  Porro  telescope  fully  up  to  the  power 
and  capacity  of  that  of  the  simpler  construction,  there  are  the  con- 
stant disadvantages  of  using  a  powerful  microscope,  which  must 
be  more  or  less  fatiguing  to  the  eyes  of  the  observer;  and  the  accumu- 
lation of  dust  on  the  inner  lens,  a  difficulty  that  may  lead  to  consid- 
erable trouble  and  annoyance.  These  reasons  have  been  more  than 
sufficient  to  prevent  the  anallatic  telescope  from  being  generally 
introduced  and  practically  used.  It  is  granted,  however,  that,  as  a 
precise  instrument,  it  is  perfectly  within  the  reach  of  the  optical 
and  mechanical  arts  to  build  one  that  shall  fully  accomplish  the 
translation  of  the  anallatic  point  to  the  center  of  the  instrument." 


CHAPTER  II 


THE  STADIA  FORMULA 

Derivation  of  Formula,.  The  value  (B—f)  in  Eq.  (4), 
for  any  ordinary  telescope  arranged  as  a  telemeter  is,  as  has 
been  shown,  proportional  to  the  intercept  S  on  a  rod  held 
vertically.  In  other  words,  sighting  horizontally,  the  par- 
allel cross-hairs  of  the  telescope  will  intercept  a  space  on  a 
rod  proportional  to  the  distance  at  which  the  rod  is  held 


FIG.  5. 

from  a  point  which  lies  an  object-glass  principal  focal  length 
in  front  of  the  object-glass  of  the  telescope. 

Let  c,  Fig.  5,  represent  the  distance  measured  along  the 
tube  of  the  telescope  from  the  vertical  axis  or  center  of  the 
instrument  to  the  object-glass. 

Then  for  a  horizontal  sight 


D=B+c; 


or 

From  (4) 
Calling 


c+f=e, 


(5) 
(6) 
(7) 
(8) 


10  TOPOGRAPHIC  STADIA  SURVEYING 

which  is  allowable  because  the  value  c,  being  affected  only 
by  the  movement  of  the  object-glass  in  focusing  upon  the 
rod  is  for  practical  purposes  to  be  regarded  as  a  constant, 
Eq.  (7)  becomes 

D=e+KS (9) 

This  is  the  fundamental  formula.  K  is  called  the  rating 
factor  and  e  may  for  convenience  be  called  the  instrument 
constant. 

The  values  of  c  and  of  /,  and,  therefore,  the  value  of  e, 
can  always  be  directly  measured  with  sufficient  precision;  / 
in  the  instrument  of  the  ordinary  type  with  single  objective 
is  the  length  of  that  portion  of  the  telescope  tube  between  the 
objective  glass  and  the  cross-hairs,  when  the  telescope 
has  been  focused  upon  a  distant  object.  The  value  of  c 
may  be  determined  also  by  measurement  when  the  tele- 
scope is  focused  upon  some  object  about  50  ft.  distant. 

Determination  of  the  Rating  Factor.  When  a  telescope 
has  fixed  cross-hairs  and  the  value  of  e  has  been  ascertained 
the  instrument's  rating  factor  is  determined  as  follows: 

Measure  from  the  vertical  axis  of  the  instrument  as  follows: 

To  point  Pi  at  (100  +e)  ft.; 
To  point  P2  at  (200  +e)  ft.; 
To  point  P3  at  (300  +e)  ft.- 

etc.  etc. 

To  point,  Pio  at  (1000 +e)  ft. 

The  selected  ground  for  such  a  determination  must  be 
such  that  all  of  the  readings  can  be  made  with  a  horizontal 
telescope  otherwise  the  rod  must  be  held  normal  to  each  line 
of  sight  and  the  distance  measured  on  the  ground  must  be 
parallel  with  this  line  of  sight. 

The  rod  being  held  at  each  of  the  ten  points  there  will  be 
obtained  ten  rod  readings  (each  foot  on  the  rod  being  read 
as  100  ft.).  These  readings  are  now  divided  in  their  order 
by  1,  2,  by  3,  etc.,  by  10.  Each  quotient  will  be  an  observed 


TOPOGRAPHIC  STADIA  SURVEYING  11 

value  of  the  instrument's  rating-factor.  The  mean  of  the 
observed  values  is  to  be  accepted  as  the  value  of  K.  No 
individual  observation  should  vary  more  than  0.2%  from  the 
mean. 

100 

The  stadia  unit  is  then  —7-  ft. 
A 

For  example:  Suppose  K  =80  then  V0/  =  1.25  ft.,  the  stadia 
unit.  If  now  a  rod  based  on  the  subdivision  of  1.25  ft.  in- 
stead of  1  ft.  as  the  unit  be  prepared  for  use  with  the  tele- 
scope whose  stadia  unit  is  1.25,  then  each  such  unit  may  be 
read  as  100  ft. 

Calling  the  stadia  unit  u,  its  value  is 


but 

D=e+KS;        .......     (9) 

therefore 

D=e+100-  .......     (11) 

u 

The  distance  in  feet,  in  other  words,  will  be  the  instru- 
ment constant  plus  100  times  the  intercept  measured  in  stadia 
units. 

Whenever  a  rod  has  a  stadia-unit  other  than  one  foot,  some 
scheme  of  rod  subdivision  and  marking  should  be  used  that 
will  enable  an  easy  identification  of  the  rod,  which  is  in  this 
event  to  be  used  only  with  a  particular  instrument,  and  only 
for  stadia  and  vertical  angle  work  —  not  for  any  ordinary 
leveling. 

When  the  cross-hairs  of  the  telescope  are  adjustable  they 
can  be  set  so  that  the  rating  of  the  instrument  will  be  con- 
venient, usually  1  to  100. 

To  adjust  the  cross-hairs  measure  from  the  center  of  the 
instrument  to  a  distance  about  equal  to  the  average  length 
of  a  sight  making  the  same  some  multiple  of  100  ft.  in- 


12  TOPOGRAPHIC  STADIA  SURVEYING 

creased  by  the  instrument  constant  as,  for  instance  (400  -f-e)  ft. 
The  cross-hairs  are  now  so  adjusted  that  the  intercept 
between  the  lower  and  the  upper  hairs  when  sighting  with  a 
horizontal  telescope  will  be  exactly  4  ft.  and  that  the  middle 
cross-hair  will  exactly  bisect  this  intercept.  The  rating  of 
the  instrument  is  thus  made  1  to  100.  If  so  convenient  a 
rating  factor  as  100  is  not  practical  the  cross-hairs  may,  of 
course,  be  so  adjusted  that  the  intercept  will  have  to  be 
multiplied  by  some  other  round  number — such  as  50,  150  or 
200— to  make  the  product  400. 

After  the  cross-hairs  have  been  adjusted  with  the  rod  at 
some  such  distance  as  (400  +e),  or  (500  -f-e),  or  (600  +e)  ft., 
readings  should  be  taken  at  other  measured  distances,  as  for 
example  at  one-half  the  distance  first  selected  and  at  a  point 
at  twice  this  distance,  in  order  to  give  a  check  upon  the 
accuracy  to  be  expected.  The  error  in  an  individual  sight 
for  adjustment  under  assumed  favorable  atmospheric  con- 
ditions, should  not  exceed  0.2%,  if  the  instrument  is  intended 
for  use  in  ordinary  topographic  surveying. 

It  may  be  repeated  that,  for  the  instrument  with  fixed 
cross-hairs,  either  the  rating  factor  must  be  determined,  as 
explained,  and  used  in  estimating  distances  from  readings 
on  a  rod  with  the  measuring  unit  (one  foot),  as  the  subdi- 
vision unit,  or  in  the  manner  already  described  the  stadia 
unit  is  calculated  from  observations  and  a  special  rod  is 
constructed  for  use  with  that  instrument  only.  The  latter 
is  rarely  a  desirable  procedure. 

General  Formulas  for  Inclined  Sights.  When  the  transit, 
or  the  alidade  of  the  plane-table  are  used  to  measure  both 
distance  and  difference  in  elevation,  the  rod  may  be  held 
either  normal  to  the  line  of  sight  or  vertical.  In  the  first 
case  the  length  of  the  inclined  line  from  the  instrument  to 
the  sighting  point  on  the  rod  is  measured.  In  the  second  case 
a  reading  is  obtained  from  which  the  horizontal  distance 
to  the  rod  and  the  difference  in  elevation  may  be  calculated. 
The  advantages,  for  all  ordinary  surveying,  of  the  second 


TOPOGRAPHIC  STADIA  SURVEYING 


13 


method,  as  illustrated  in  Fig.  6,  are  so  pronounced  that  it  is 
not  necessary  to  discuss  the  use  of  the  inclined  rod. 

In  Fig.  6  the  intercept  on  a  rod  held  vertically  at  the  point 
P  is  S.  The  vertical  angle,  when  the  middle  cross-hair  is 
set  on  the  sighting-point  P',  is  a. 

It  is  to  be  remembered,  as  already  stated,  that  throughout 
this  manual,  except  when  otherwise  noted,  instruments 
rated  1  to  100  are  referred  to.  For  such  instruments  the 


FIG.  6. 


rod-reading,  as  entered  in  the  notes  of  the  surveyor,  will 
be  100  S.  When  instruments  have  some  other  rating  the 
value  'KS  may  be  substituted  for  the  rod-reading  (i.e.,  for 
100  S.) 

Referring  again  to  Fig.  6,  it  will  be  seen  that  if  the  rod  had 
been  held  through  the  point  P7  normal  to  the  axis  of  the 
telescope,  the  intercept  would  have  been  HH',  instead  of  S. 
The  length  of  HH'  establishes  the  length  of  the  inclined 
line  IP',  and  the  line  IP'  together  with  the  vertical  angle 


14  TOPOGRAPHIC  STADIA  SURVEYING 

a  enables  a  calculation  of  the  horizontal  distance  D  and  of  the 
difference  of  elevation  h  to  be  made. 

HH'=S  cos  a  (very  nearly);     ....     (12) 
IP' =  100  S  cos  a+e;  (13) 

D  =  (100  S  cos  «+e)  cos «;        .     .     .     (14) 
and 

h  =  (WQS  cos  <*+e)  sine*.         .     .     .     (15) 

Calling  the  rod  reading 

100  S=r;        (16) 

will  make 

D=r  cos2  a+e  coo  a; (17) 

h=r  sin  a  cos  a+e  sin  «;     ....     (18) 
which  is 

h=r(%  sin  2a)+e  sin  a (19) 

These  are  the  formulas  in  ordinary  and  in  general  use  for 
the  determination  of  distance  and  difference  in  elevation 
with  a  stadia  instrument.  They  are  not  strictly  correct, 
because  Eq.  (12)  is  not  mathematically  correct.  The  line 
HH'  normal  to  the  collimation  axis  of  the  telescope  is  not 
normal  to  the  two  lines  IH  and  IH',  between  which  the  inter- 
cept lies.  These  lines  in  the  case  of  an  instrument  rated  at 
100  enclose  an  angle  of  about  34'.  Each  of  these  lines  departs 
from  the  line  of  sight  by  about  IT.  It  follows  that  while 
HP'  is  exactly  equal  to  H'P'  the  intercept  S  is  not  exactly 
bisected  by  the  middle  cross-hair,  there  being  in  the  small 
triangle  BHP'  and  B'H'P'  (see  Fig.  7)  an  acute  angle  at  H 
of  about  89°  43',  while  at  H'  in  the  other  small  triangle  the 
angle  is  obtuse,  90°  17'. 

It  can  readily  be  shown  that  the  error  made  in  accepting 
Eq.  (12)  is  so  small  that  it  is  negligible.  In  order  that  this 
may  become  apparent  the  following  is  presented.  Referring 


TOPOGRAPHIC  STADIA  SURVEYING 


15 


to  Fig.  7,  draw  the  lines  HA  and  H'A'  perpendicular  to  HH' 
then 


HA=H'A'=-sma. 


(20) 


FIG.  7. 

In  the  triangle  HAB  the  angles  will  be,  for  an  instrument 
rated  at  100: 

At//,  17'; 
At  A,  90°  -a- 
AtB,  90°+a-17'. 

In  the  triangle  H'A'B'  the  angles  will  be 

At//',  17'; 
At  A',  90° +a; 
AtB',  90° -o-17'. 


Therefore 


sin  17' 


.     .     .     (21) 


16  TOPOGRAPHIC  STADIA  SURVEYING 

A'B>-2a*a-r     Slnl7/  (22) 

2  sin  (89°  43'  -a) 

and  because 

'  =  (S-A'B'+AB)cosa;     ....     (23) 

**^^^:^  (24) 

and 


+ecosa.      .      (25) 

The  error  that  results  in  using  formula  (14)  or  (17)  in  place 
of  formula  (25)  will  be 


Based  on  this  equation  it  appears  that  the  inaccuracy  of 
Eq.  (17)  is  as  follows: 
For 

a  =  10°  the  error  will  be  only  .00007%; 

a  =20°  the  error  will  be  only  .0003%; 
a  =  30°  the  error  will  be  only  .0008%; 
a  =45°  the  error  will  be  only  .0025%. 

These  errors  are,  as  already  stated,  too  small  to  be  taken 
into  account. 

Approximation  Formulas.  The  value  of  e  is  generally 
small.  It  will  rarely  exceed  2  ft.  and  will  generally  be  nearer 
1  ft.  This  being  the  case  there  will  be  only  a  slight  error 
introduced  if  in  formulas  (17)  and  (18)  the  value  e  be  replaced 
by  e  cos  a.  This  substitution  is  certainly  allowable  in  all 
ordinary  topographic  surveying  operations,  in  which  dis- 
tances are  required  only  to  the  nearest  foot. 


TOPOGRAPHIC  STADIA  SURVEYING  17 

With  this  modification  the  formulas  (17)  and  (18)  become 
D  =  (r  +e)  cos2  a  (approximate)  ;  .  .  .  .  (27) 
h  =  (r+e)  sin  a  cos  a  (approximate).  .  .  (28) 

In  this  form  the  formulas  are  very  convenient. 

The  expressions  (r-\-e]  cos2  a  and  (r+e)  sin  a  cos  a  in 
these  equations  and  the  expressions  r  cos2  a  and  r  sin  a  cos  a 
in  Eq.  (17)  and  (18)  are  such  that  they  can  conveniently 
be  obtained  from  diagrams,  as  will  hereinafter  be  explained. 

The  practice  of  disregarding  entirely  the  distance  incre- 
ment e  cos  a  in  formula  (17),  and  the  elevation  increment 
e  sin  a  in  formula  (18)  can  not  be  endorsed.  Although, 
as  is  well  known,  the  error  of  the  individual  moderately  long 
sight  is  frequently  in  excess  of  the  value  of  e,  the  effect  of 
ignoring  the  correction  altogether  would  be  cumulative,  a 
source  of  error  which  is  not  allowable  when  locating  primary 
or  secondary  stations. 

There  is  less  objection  to  doing  this  when  side  shots  for 
ground  elevation  only  are  involved.  In  this  case  the  author's 
practice  has  always  been  to  enter  the  reduction  diagram, 
hereinafter  described,  with  a  value  (r+1).  One  foot  is  a 
sufficiently  close  approximation  of  the  value  of  e  for  all 
ordinary  surveying  instruments. 

For  unimportant  side  shots,  such  as  shots  for  elevation 
of  the  ground,  the  following  approximations  can  therefore 
be  recommended: 


cos2«;          ......     (29) 

sin  «  cos  a  ......     (30) 

Suggestions    Relating    to    the    Use    of   the    Formulas. 

In  reducing  the  field  observations  it  will  be  well  to  be  guided 
by  the  following  suggestions: 

1.  Use  the  correct  formulas  (17)  and  (18)  in  making  sur- 
veys which  require  the  greatest  attainable  accuracy. 


18  TOPOGRAPHIC   STADIA  SURVEYING 

2.  Use  the  approximation  formulas   (27)   and   (28)   and 
stadia  reduction  tables  for  foresights  and  backsights  and.  for 
sights  to  reference  points. 

3.  Use  the  approximation  formulas  (27)  and  (28)  or  (29) 
and  (30)  and  a  slide  rule  or  such  diagrams  as  accompany 
this  manual  for  all  ground  heights  and  general  topography. 

In  order  that  the  accuracy  attainable  by  use  of  the  approx- 
imation formulas  (27)  and  (28)  may  be  correctly  gaged,  it 
is  to  be  stated  that  their  use  introduces  errors  as  follows: 

When  e  =  1.5  ft.  the  error  in  distance  will  be  less  than  0.1 
ft.  for  all  vertical  angles  less  than  20°;  it  will  be  -0.2  ft. 
for  a  vertical  angle  of  30°,  and  -0.3  ft.  for  a  vertical  angle 
of  45°.  The  error  in  elevation  will  be  less  than  0.1  ft.  for  all 
vertical  angles  less  than  30°  and  it  will  be  —0.3  ft.  for  a 
vertical  angle  of  45°. 

For  values  of  e  other  than  1.5  ft.  the  errors  can  readily  be 
approximated  from  the  foregoing,  as  they  increase  or  decrease 
proportionately  with  e. 


CHAPTER  III 

DIAGRAMS  FOR  THE  REDUCTION  OF  STADIA 
MEASUREMENTS 

Diagrammatic  Solution  of  Stadia  Formulas.  The  fol- 
lowing considerations  have  led  to  the  preparation  of  diagrams 
for  the  determination  of  values  for  the  expressions  r  cos2  a 
and  r  sin  a  cos  a  in  Eq.  (17)  and  (18),  (r+e)  cos2  a  and  (r+e) 
sin  a  cos  a  in  the  approximation  formulas  (27)  and  (28)  and 


for  the  expressions  (r+1)  cos2  a  and  (r  +  1)  sin  a  cos  a  in  the 
approximation  formulas  (29)  and  (30). 
In  any  circle  whose  radius  is  OP,  Fig.  8,  there  will  be 

/P=7Lcos«; 
IP'  =IL  cos2  «; 
PL=IL  sin  «: 
PP'  =7L  sin  a  cos  a. 

If  IL,  the  diameter  of  the  circle  be  made  equal  to  r  or  to 
(r+e)  or  to  (r  +  1),  according  to  the  formulas  to  be  used, 

19 


20 


TOPOGRAPHIC  STADIA  SURVEYING 


5    g    g    S    S    S    si 


STADIA   DIAGRAM 


For  Instruments  rated  1  to  1OO 


Graphical  Solution  of  the  Approximation  Formolas:- 

D=(r*OcosV  D^r+Ocos1 

h=(r+e)  sineccosa  *   h-(r+l) 

Where: 

rereading  on  a  vertical  rod 
«  -vertical  angle. 
D-feorizontal  distance. 
h=difference  in  elevation. 


constant=lhe  distance 
of  the  outside  focal  point  of  the 
object  lens  from  the  instrument 
axis. 


Follow  the  vertical  angle  ray  to 
the  curved  line  (r-e)  or  (M) 
as  the  case  may  DC  and  read 
D  on  the  horizontal  scale 
and  h  on  the  veitical  scale. 


—      rOo-i-F»<-ncr>.-jcDcO 
oo     o     oo     o     o     oo 


TOPOGRAPHIC  STADIA  SURVEYING  21 

the  lifte  IP'  will  represent  the  distance  increment  and 
PP'  the  difference  of  elevation  increment  in  the  above 
formulas. 

If,  now,  for  all  possible  values  of  r,  or  of  (r+e),  or  of  (r  +  1) 
as  the  case  may  be,  a  series  of  semicircles  be  drawn  all 
having  a  common  point  I,  each  circle  will  be  the  focus  of  the 
points  P  determined  by  all  possible  values  of  the  vertical 
angle  and  a  value  of  r,  or  of  (r+e},  or  of  (r+1),  equal  to  the 
diameter  of  each  circle.  In  other  words,  for  any  vertical 
angle  «  the  limiting  side  line  of  the  angle,  or  the  angle  ray, 
will  cut  the  circle  at  a  point  P  such  that  the  horizontal  line 
IP'  or  I'P  will  be  the  value  as  the  case  may  be  of  r  cos2  a,  or 
of  (r+e)  cos2  a,  or  of  (r+1)  cos2  a,  and  that  PP' will  be  the 
value  of  r  sin  a  cos  a,  or  of  (r+e)  sin  a  cos  a,  or  of  (r+1)  sin 

a  COS  a. 

Semicircles  with  diameters  increasing  by  regular  amounts 
1  ft.,  or  2  ft.,  or  5  ft.,  or  10  ft.,  according  to  scale,  and  hori- 
zontal lines  forming  a  scale  by  which  to  read  off  difference  in 
elevation  and  vertical  lines  by  which  to  read  off  distance, 
complete  the  diagram. 

To  secure  accuracy  in  scaling  difference  in  elevation  the 
unit  of  the  vertical  scale  may  be  made  larger  than  the  unit 
of  the  horizontal  scale.  The  semicircles  will  then  be  ellipses. 
According  to  the  scales  adopted  any  reasonable  degree  of 
accuracy  can  be  attained.  (See  Fig.  9.) 

For  ordinary  topographic  surveying  the  stadia  diagram 
accompanying  this  manual  will  be  found  adequate  to  fill 
every  requirement.  This  diagram  is  so  arranged  that  both 
difference  in  elevation  and  correct  horizontal  distance  can 
be  read  at  the  same  point.  The  diagram  has  been  drawn, 
in  the  main,  to  logarithmic  scales  in  order  that,  for  practically 
all  distances  the  relative  accuracy  of  results  obtained  by  its 
use  will  be  substantially  the  same.  The  distances  shown  on 
the  diagram  are  from  100  to  1000  feet.  They  might  have 
been  called  10  to  100  or  1  to  10  feet  with  a  corresponding 
modification  of  the  difference  in  elevation.  The  scale  from 


22  TOPOGRAPHIC  STADIA  SURVEYING 

100  to  1000  feet  was  adopted  because  the  largest  number  of 
sights  will  ordinarily  fall  between  these  limits. 

The  curved  lines  in  the  diagram  represent  all  possible 
values  of  r,  of  r+e,  or  of  r+1. 

In  using  the  diagram  the  same  care  must  be  exercised  in 
placing  the  decimal  point  correctly  as  in  the  case  of  slide 
rule  work.  It  is  to  be  noted  that  in  any  region  in  which  oro- 
graphic  features  are  pronounced  it  would  be  useless  to 
attempt  to  measure  elevations  with  greater  precision  than 
to  the  nearest  foot.  They  may,  of  course,  be  read  from  the 
diagram  and  entered  in  the  notes  to  tenths,  but  should  in 
such  case  appear  on  the  map  without  fractional  feet. 

The  Diagram  Furnished  with  this  Manual.  The  dia- 
gram for  the  reduction  of  stadia  notes  which  accompanies 
this  manual  is  prepared  specifically  as  a  graphic  solution  at 
one  operation  of  the  approximation  formulas. 

D  =  0+e)  cos2«; (27) 

and 

h  =  (r+e)  sin  a  cos  a.       .     .     .     (28) 

But  the  diagram  may  also  be  used  in  ascertaining-  the 
values  of  r  cos2  a  and  r  sin  a.  cos  a  in  the  correct  formulas  Eq. 
(17)  and  (18)  and  for  the  approximation  of  (r+1)  cos2  a.  and 
of  (r+1)  sin  a  cos  a  in  the  approximation  formulas  (29)  and 
(30).  As  the  formulas  (17)  and  (18)  need  only  be  used  for 
sights  to  turning  points  and  on  surveys  requiring  more  than 
ordinary  precision,  it  would  seem  advisable  to  give  prefer- 
ence to  reduction  tables  whenever  such  approximation  for- 
mulas as  (27)  and  (28)  or  (29)  and  (30)  will  not  serve. 

To  Use  the  Diagram.  Follow  the  ray  which  corresponds 
to  the  angle  a  of  elevation  or  depression  to  its  intersection 
with  the  curved  line  which  corresponds  to  the  value  (r+e) 
in  formulas  (27)  and  (28).  Holding  a  needle  point  at  the 
intersection  thus  determined  read  off  on  the  vertical  lines 
the  horizontal  distance  D,  that  is  (r+e)  cos2  a,  and  on  the 


TOPOGRAPHIC  STADIA  SURVEYING  23 

horizontal  lines  the  difference  in  elevation  h,  that  is  (r-fe) 

Sin  a  COS  a. 

Thus  when  the  approximation  formulas  are  to  be  used,  the 
diagram  gives  at  once  the  distance  and  the  difference  in 
elevation  for  any  rod-readings  and  any  vertical  angles 
within  their  scope.  Distance  should  be  read  to  the  nearest 
foot  and  difference  in  elevation  to  the  nearest  tenth  of  a  foot. 

When  points  are  located  by  the  intersection  of  sights  from 
two  instrument  stations,  the  horizontal  distances  from  each  of 
these  two  stations  are  scaled  from  the  map.  The  diagram  is 
now  entered  with  each  of  these  distances  and  needle  points 
are  placed  at  the  intersection  of  these  distances  with  the 
corresponding  angle  rays  of  the  measured  angles  of  elevation 
or  depression.  If  the  same  difference  of  elevation  is  not 
indicated  by  both  needle  points  the  mean  value  should  be 
recorded. 


CHAPTER  IV 

THE  SLIDE-RULE  AS  AN  AID  IN  REDUCING 
STADIA  NOTES 

Modification  of  Formulas  for  Slide-rule  Work.     It  is 

not  always  convenient  to  use  a  diagram  in  reducing  rod- 
readings  and  vertical  angles  to  distance  and  elevation  dif- 
ference. This  is  particularly  true  for  plane-table  work 
which  requires  that  the  reduction  be  made  in  the  field.  In 
such  cases  slide-rules  may  be  used  to  advantage.  Special 
slide-rules  are  made  for  the  purpose.  These  need  not  receive 
any  special  notice.  But  the  ordinary  slide-rule  can  be  made 
a  convenient  aid  as  will  now  be  shown. 

Formulas  (17)  D  =r  cos2  a-\-e  cos  «; 

(18)  h=r  sin  a  cos  «  +  e  sin  «; 

and  (27)  D  =  (r+e)  cos2  a  (approximate); 

(28)  h  =  (r  +e)  sin  a  cos  «  (approximate) ; 

can  be  made  convenient  for  solution  with  the  slide-rule  by 
substituting  for  sin  a  cos  a  the  trigonometric  equivalent 

sin  a  cos  «  =|  sin  2a (31) 

For  work  with  the  slide-rule  only  the  approximation  for- 
mulas   (27)    and    (28)    or    (29)  and    (30)  should    be   used. 

24 


TOPOGRAPHIC  STADIA  SURVEYING  25 

In    combination  with    (31)    the   Eqs.    (27)   and    (28)    will 
become : 

D  =  (r+e)  cos2  a; (27) 

h  =——  sin  2a. 

Both  of  these  equations  or  similar  equations  containing 
the  factor  (r+1)  are  readily  solved  with  the  ordinary  slide- 
rule. 


CHAPTER  V 
METHODS  OF  STADIA  SURVEYING 

Stadia  Surveys  Without  the  Use  of  the  Magnetic 
Needle.  When  the  plane-table  or  transit  are  oriented 
without  the  use  of  a  magnetic  needle,  the  instrument  is  to 
be  set  up  over  a  starting  point  of  known  position  and  eleva- 
tion. The  height  i  of  the  telescope  above  the  bench-mark  or 
station-plug  is  measured  and  the  table  or  transit  are  oriented. 
The  first  orientation  is  adapted  to  the  shape  of  the  area  to 
be  covered  or  to  other  considerations.  It  may,  of  course,  be 
based  on  a  north  point  determination.  At  all  subsequent 
settings  the  plane-table  or  the  lower  plate  of  the  transit,  as 
the  case  may  be,  must  be  brought  into  a  position  parallel 
with  the  first  setting.  To  accomplish  this  in  the  case  of  the 
transit,  after  setting  the  vernier  at  the  azimuth  which  was 
read  at  the  last  station  (when  sighting  toward  the  new  sta- 
tion), and  reversing  the  telescope,  a  sight  is  taken  back  toward 
the  last  station,  whereby  the  lower  plate  of  the  transit  is 
brought  into  the  desired  position.  In  the  case  of  the  plane- 
table  the  operation  is  similar,  the  ruler  of  the  alidade  being 
reversed  along  the  last  station  sight. 

At  each  setting  the  height  i  of  the  telescope  above  the 
station  plug  is  measured.  This  height  determines  the  eleva- 
tion of  the  telescope  the  "  height  of  instrument  "  in  case  this 
should  be  required.  Ordinarily,  this  will  not  be  required,  all 
sights  being  taken  for  vertical  angles  to  the  point  i  on  the  rod 
as  determined  for  each  instrument  setting.  Differences  in 
elevation  as  then  determined,  regardless  of  the  value  of  i, 
are  thereupon  applied  directly  to  the  plug  elevation  of  the 

26 


TOPOGRAPHIC  STADIA  SURVEYING  27 

instrument  station.  Only  when  level  sights  are  taken  and 
the  rod  is  read  direct  for  elevation  will  it  be  necessary  to 
apply  the  readings  to  the  height  of  instrument,  which  is, 
of  course,  the  elevation  of  the  station  plug  plus  i. 

The  rule  should  be  carefully  observed  to  let  the  last  sight 
recorded  at  any  station  be  the  sight  to  the  next  station  to  be 
occupied. 

From  each  station  as  occupied  there  will  first  be  the  orien- 
tation of  the  transit  or  plane-table.  In  sighting  back  upon 
the  last  station  occupied  the  rod  should  again  be  read  for 
distance  and  the  vertical  angle  should  be  noted.  The  survey 
is  thus  checked.  The  mean  of  the  two  observations,  if  there 
be  no  palpable  error,  should  be  used  in  determining  position 
and  elevation  of  the  new  station. 

As  a  variant  of  the  foregoing  the  transit  may  be  used  at 
each  station  to  determine  the  azimuth  of  all  sights  taken  in 
their  relation  to  the  backsight.  In  this  case  the  vernier  is 
set  at  zero  when  taking  the  backsight  for  orientation. 

Each  instrument  station  should  be  at  such  distance  from 
the  preceding — topographic  features  being  considered — 
that  it  will  command  a  fair  amount  of  new  territory.  A 
foresight  of  the  length  of  ordinary  sights  for  topographic 
points  would  place  the  new  station  at  the  margin  of  the  terri- 
tory already  commanded.  In  some  cases  it  may  be  advisable 
simply  to  make  the  foresight  as  long  as  consistent  with  the 
accuracy  required.  In  other  cases  it  may  be  of  advantage 
to  treat  alternate  stations  as  secondary  stations  using  them 
only  for  the  purpose  of  locating  the  next  primary  station 
farther  on. 

Referring  to  stadia  surveys,  Noble  and  Casgrain,  in  the 
introduction  to  their  tables  for  horizontal  distance  and 
difference  of  level,*  say:  "The  height  of  instrument  can  be 
determined  from  the  backsight,  or  the  instrument  can  be 
set  over  a  point  whose  height  has  been  determined  and  the 

*  A.  Noble  and  W.  T.  Casgrain.  Tables  for  Horizontal  Distance 
,  and  Difference  of  Level.  Eng.  News  Pub.  Co.,  1902. 


28  TOPOGRAPHIC  STADIA  SURVEYING 

height  of  the  telescope  above  it  is  measured  directly  by  a 
light  graduated  rod  carried  for  the  purpose.  The  latter  is  the 
usual  method." 

Stadia  Surveys  with  the  Use  of  the  Magnetic  Needle. 
When  the  magnetic  needle  (or  a  solar  compass)  is  used 
in  orienting  the  transit  or  the  plane-table,  or  in  determining 
the  azimuth  of  the  sights  taken  with  the  transit,  a  different 
method  of  surveying  is  made  possible.  The  intermediate 
or  secondary  stations  can  be  treated  as  turning-points. 

The  instrument  is  not  set  up  at  all  at  the  secondary  stations. 
But,  in  this  case,  the  double  sighting  between  stations  is  no 


__ k 


longer  possible  and  recourse  should  be  had  to  some  other 
method  of  checking  the  observations.  Probably  the  best 
method  of  accomplishing  this  is  by  using  two  intermediate 
stations,  preferably  so  selected  that  the  angle  between  the 
two  foresights  to  these  stations  will  be  at  least  30°.  As  all 
stadia  work  should  be  done  with  two  or  more  rodmen  there 
is  usually  no  difficulty  in  adopting  this  double-turning-point 
method.  Two  locations  and  two  elevations  of  each  primary 
station  will  thus  be  obtained.  Barring  gross  errors,  the 
mean  of  the  elevations  and  of  the  positions  of  the  new  instru- 
ment station  thus  determined  should  be  accepted.  (Correc- 
tions can  be  carried  back,  if  desired,  to  the  two  secondary 
stations.) 


TOPOGRAPHIC  STADIA  SURVEYING  29 

Fig.  10  illustrates  a  set  of  sights  of  this  kind.  The  broken 
lines  show  the  sights  as  taken;  the  full  lines  as  they  will 
appear  when  corrected. 

The  method  of  keeping  notes  for  a  transit  survey  by  the 
double-turning-point  method  is  illustrated  on  page  40. 


CHAPTER  VI 
PRACTICAL  SUGGESTIONS 

Departures  from  Ordinary  Practice.  The  author  has 
found  several  departures  from  the  ordinary  methods  of 
stadia  surveying  advantageous  and  recommends  them  to 
those  who  have  occasion  to  use  the  stadia.  These  depar- 
tures, including  some  modifications  of  methods  already 
alluded  to,  relate: 

1.  To  the  type  of  rod. 

2.  To  the  elimination  from  the  notes  of  the  height  of  the 
telescope  above  a  station  plug. 

3.  To  the  liberal  use  of  the  magnetic  needle. 

4.  To  the  method  of  keeping  field  notes. 

5.  To  the  use  of  approximation  formulas. 

6.  To  the  use  of  convenient  stadia  reduction  diagrams. 
The  Stadia  Rod.     The  rod  which  is  here  described  was 

designed  and  its  markings  were  devised  about  1880  in  the 
office  of  the  State  Engineer  *  of  California.  No  one  will  be 
surprised  or  misled  when  the  author,  under  whose  super- 
vision the  first  rod  of  the  kind  was  made,  states  that  he  has 
found  no  other  self-reading  rod  equally  satisfactory  for  gen- 
eral use.  The  rod  is  presented  on  its  merits,  without  prejudice 
to  other  self-reading  rods  of  which  many  more  or  less  satis- 
factory types  are  on  the  market. 

The  rod  is  shown  in  Figs.  11  to  16.  It  is  a  folding  rod, 
being  cut  midway  of  its  length,  so  that,  when  folded,  the 
painted  face  of  the  rod  will  be  protected  against  injury. 

*  Wm.  Hammond  Hall  was  at  that  time  the  State  Engineer  of 
California. 

30 


TOPOGRAPHIC  STADIA  SURVEYING 


31 


Stiffness  when  extended  is  secured  by  means  of  a  light  board, 
Fig.  11,  with  projecting  overlapping  edges.  The  hinges  are 
relieved  of  all  strain  by  this  arrangement. 

Into  the  back  of  the  stiffening  board  are  set  two  small 
plates  of  iron  with  round  holes  through  which,  and  through 


FIG.  11.— The  stiffen- 
ing board. 


FIG  12. 


I 

tJ 

FIG.  13.— The  folded 
rod. 


the  board  and  through  the  rod,  thumb-screws  pass  to  similar 
plates  with  threaded  holes  in  the  face  of  the  rod. 

The  type  of  thumb-screw  to  which  preference  has  been 
given  by  the  author  was  turned  from  a  round  bar  of  iron, 
as  shown  in  Fig.  12.  A  small  bar  through  the  head  of  the 
screw  gives  ample  leverage  for  setting  the  screws  tight,  which 
is  a  matter  of  no  small  importance.  The  rod  when  extended 


32  TOPOGRAPHIC  STADIA  SURVEYING 


FIG.  15. — Two  types  of  rod.    A.  For 
ordinary  use.    B.  For  long  sights. 


FIG.  14.— Stadia  rod. 


TOPOGRAPHIC  STADIA  SURVEYING  33 

should  have  no  lost  motion  at  the  central  joint.  Thumb- 
screws of  the  type  described,  cut  from  about  f.  in.  iron,  will 
stand  much  rough  handling. 

When  folded  up  the  stiffening  board  is  shifted  to  near  the 
end  of  the  rod,  Fig.  13,  where  there  are  holes  for  the  free 
passage  of  the  thumb-screws  through  one  leaf  of  the  folded 
rod  into  the  threaded  holes  of  two  more  small  iron  plates  set 
in  the  opposing  face  of  the  other  leaf.  The  thumb-screws 
here  not  only  hold  the  stiffening  board  securely  in  place,  but 
clamp  the  two  leaves  of  the  rod,  so  that  there  can  be  no  sliding 
of  face  against  face.  In  its  folded  condition  the  rod  is  excep- 
tionally well  protected  and  will  stand  much  handling  without 
injury. 

The  preferred  length  has  always  been  11  or  12  ft.  but 
shorter  or  longer  rods  may  be  found 
convenient.  The  folded  length  is  just 
one-half  of  the  full  rod  length.  The 
top  and  bottom  of  the  rod  should  be 
shod  with  strips  of  iron,  though  in 
the  case  of  the  top,  lighter  iron  than 
in  the  case  of  the  bottom  may  be  FIG.  16.— A  two-tenth 
used.  rod  increment. 

The  width  of  the  rod  should  be  at 

least  3£  in.  It  may,  at  pleasure  and  to  advantage,  be  made 
somewhat  wider. 

Any  type  of  lettering  and  subdivision  may  now  be  used, 
but  one  which  is  not  likely  ever  to  be  abandoned  if  once 
tried,  particularly  by  those  who  delight  in  using  home-made 
rods,  is  the  one  shown  in  Figs.  14,  15,  and  16.  When  the  rod 
is  wider  than  3|  ins.  the  spaces  marked  f  in.  Fig.  16,  should  be 
increased  somewhat.  A  longer  oblique  line  than  shown,  for 
the  interpolation  of  hundredths  of  a  foot,  will  be  found 
advantageous. 

The  reading  is  to  the  nearest  hundredth  of  a  foot  along  the 
oblique  lines  of  the  black  triangle.  The  figures  cut  by  the 
cross-hair  are  always  read;  they  stand  on  the  footmarks. 


34  TOPOGRAPHIC  STADIA   SURVEYING 

The  black  rectangle  of  the  odd  tenths  backed  by  a  black 
triangle,  together  with  the  superimposed  triangle  of  the  next 
even  tenth  make  a  characteristic  design,  Fig.  16,  which 
helps  the  eye  to  mount  from  point  to  point  with  certainty 
by  two-tenth  intervals.  The  tops  of  the  figures  are  always 
three-tenths  points.  The  five- tenth  points  are  indicated 
by  red  diamond-shaped  marks  and  the  full  foot  by  similar 
elongated  red  spear-heads,  or  half  spear-heads,  extending 
across  the  face  of  the  rod. 

With  telescopes  of  the  ordinary  power  a  rod  of  this  kind 
with  3|  in.  face  is  good  for  all  distances  ordinarily  entering 
into  stadia  work.  When  sights  exceeding  600  ft.  are  fre- 
quent, it  will  be  found  convenient  to  use  a  rod  with  the  sub- 
divisions of  the  feet  alternately  at  the  left  and  at  the  right 
edge  of  the  rod,  as  shown  in  Fig.  15. 

Any  sign  painter  can  paint  such  a  rod.  It  can  be  marked 
in  a  few  minutes.  On  the  white  painted  surface,  after 
drawing  the  longitudinal  line  at  the  base  of  the  triangles,  the 
foot  marks  are  to  be  laid  off  with  care,  using  a  tested  steel 
tape.  That  the  foot  marks  should  be  correct  is  of  prime 
importance.  The  zero  point  of  the  rod  should  preferably 
be  at  the  top  edge  of  the  metal  shoe,  not  at  its  bottom,  which 
is  subject  to  wear.  Using  a  pattern  cut  from  a  sheet  of  tin 
or  other  convenient  material,  one  foot  long,  the  oblique 
limiting  lines  of  all  the  black  triangles  can  be  drawn  prac- 
tically with  a  continuous  stroke.  A  stencil  may  be  used  in 
outlining  the  figures.  The  red  diamonds  may  now  be 
painted,  then  all  the  black  on  the  rod.  Sharp  outlines  of 
the  markings  can  be  secured  by  using  a  ruling  pen  before 
filling  in  with  the  brush. 

The  red  diamonds  are  convenient  identification  points  for 
short  sights.  Colors  can  not  be  distinguished  at  long  dis- 
tances, except  when  light  is  very  favorable.* 

*  A  stadia  rod  in  substantial  agreement  with  the  foregoing  speci- 
fications has  been  put  on  the  market  by  the  A.  Lietz  Co.,  Instrument 
Manufacturers,  San  Francisco,  Cal. 


TOPOGRAPHIC  STADIA  SURVEYING 


35 


For  work  requiring  very  long  sights  crosspieces  at  several 
points  of  the  rod,  projecting  beyond  its  sides,  and  a  slender 
extension  with  similar  crosspieces,  have 
repeatedly    been   found  to  be  of  great 
help. 

The  wood  used  for  such  a  rod  should 
be  straight-grain  and  well  seasoned. 
According  to  the  character  of  the  wood 
chosen,  the  thickness  of  the  rod  and  of 
the  stiffening  board  may  range  from 
about  f  in.  to  |  in. 

When  the  meter  is  the  distance  unit 
instead  of  the  foot,  the  markings  on  the 
rod  should  be  as  shown  in  Fig.  17.  Here 
again  the  eye  recognizes  at  a  glance  the 
even  and  odd  subdivisions.  The  readings 
can  be  made  to  the  nearest  tenth  of  a 
meter.  Such  a  rod  is  serviceable  for  pre- 
cise leveling. 

The  Elimination  of  the  Height  of  the 
Telescope  above  the  Instrument  Sta- 
tion Plug.  The  ordinary  method  of 
doing  stadia  work  requires  that  sights 
be  taken  for  vertical  angles  to  some  point 
on  the  rod  determined  by  the  height  i  of 
the  telescope  above  the  station  plug.  It 
will  be  found  much  more  convenient  to 
disregard  the  height  of  the  telescope 
above  the  instrument  point  altogether,* 
and  to  take  all  sights  to  the  5-ft.  mark  or  pIG  i7._A  metric 
to  some  other  selected  foot  mark  which  is  stadia  rod. 

at  about  the  ordinary  height  of  the  tele- 
scope above  the  ground.     That  this  height  need  not  be  the 
exact  height  of  the  telescope  above  the  ground  can  readily 
be  seen  and  will  be  better  understood  by  reference  to  the 
*  Dr.  W.  Jordan:     Vermessungskunde,  p.  630. 


36  TOPOGRAPHIC  STADIA  SURVEYING 

diagram  Fig.  18.  The  difference  in  elevation  between  the 
point  B  in  this  diagram  and  the  point  C  is  entirely  inde- 
pendent of  the  height  of  the  tripod  at  the  point  A.  It  can 
be  calculated  from  the  two  sights  A  B'  and  AC'.  The  height 
of  the  telescope  at  A  above  the  ground  or  above  a  plug  does 
not  have  to  be  known  at  all,  unless  the  elevation  of  the 
ground  or  of  the  plug  at  that  point  is  to  be  determined. 

When  it  happens  that  the  5-ft.  mark  is  not  visible,  the  cross- 
hair may  be  set  on  some  other  foot  mark,  making  note 
thereof,  and  proper  attention  must  be  paid  to  this  fact  when 
elevations  are  calculated. 

As  the  5-ft.  increment  of  the  rod  is  neither  added  nor  sub- 


FIG.  18. 

tracted  in  note-keeping  it  follows  that  all  instrument  station 
heights  may  be  entered  as  ground  heights,  but  that  they  are 
in  fact  fictitious.  They  are  not  the  real  instrument  heights 
nor  the  exact  ground  heights  at  the  instrument  station,  but 
are  elevations  5  ft.  lower  than  the  actual  height  of  the  instru- 
ment. It  is  just  the  same  as  though  the  sights  were  along 
the  dotted  lines  A'B  and  A'C,  Fig.  18. 

In  using  this  method  of  surveying  it  is  desirable  to  begin 
as  in  ordinary  leveling  by  letting  the  rod  be  held  at  the 
starting  point.  It  will  be  found  a  convenience,  and  the 
chance  of  error  in  platting  will  be  reduced,  if  backsights  are 
entered  in  the  notes  as  though  they  were  sights  taken  from 
the  rod  to  the  instrument. 


TOPOGRAPHIC  STADIA  SURVEYING  37 

The  Liberal  Use  of  the  Magnetic  Needle.  Before  pre- 
senting a  sample  page  of  notes  it  may  be  well  to  explain  the 
method  of  topographic  stadia  surveying  which  led  to  the 
foregoing  simplification.  In  difficult  country  it  is  often 
found  impracticable  to  select  instrument  stations  in  advance 
and  it  is  frequently  embarrassing  to  be  compelled  to  occupy 
stations  selected  by  assistants.  The  operations  of  setting 
up  and  of  orientation  consume  valuable  time.  To  eliminate 
these  disadvantages  of  the  ordinary  method  of  work — it 
being,  of  course,  assumed  that  the  necessary  triangulation 
work,  base-line  surveying  and  precise  leveling  to  establish 
reference  points  has  been  done — a  start  may  be  made  at  any 
point  of  known  position  and  elevation. 

The  starting  point  may  be  called  station  zero.  The  rod  is 
held  at  this  point  and  the  instrument  is  carried  to  the  place 
from  which  sights  can  be  taken  to  best  advantage  both  with 
a  view  to  getting  the  topography  within  reach  and  to  making 
progress  ahead. 

The  azimuth  is  now  determined  by  magnetic  needle. 
Unless,  for  some  reason,  the  instrument  point  is  to  be  pre- 
served it  need  not  be  marked  by  a  plug,  neither  is  it  necessary 
to  determine  the  ground  height  at  the  instrument  unless 
required  by  topographic  considerations.  The  instrument 
station  thus  occupied  is  Station  1.  The  next  turning  point 
located  by  needle  bearing,  by  stadia  reading  and  by  vertical 
angle  is  Station  2.  The  instrument  is  not  set  up  at  Station  2, 
but  is  carried  on  to  Station  3,  which  is  again  selected  with  a 
view  to  comprehensive  work.  The  position  of  Station  3  is 
fixed  by  direction  and  distance  from  2,  and  so  on.  Back- 
sights for  azimuth  must,  of  course,  be  taken  with  reversed 
telescope,  or  the  south  end  of  the  magnetic  needle  must  be 
read.  Care  must  also  be  taken  to  give  the  vertical  angle 
its  proper  sign.  It  will  be  noted  that  the  line  becomes  a 
continuous  traverse  line,  the  odd-numbered  stations  being 
instrument  stations,  the  others  turning  points. 

For  ground  heights  and  short  sights  reliance  may  be  had 


38  TOPOGRAPHIC  STADIA  SURVEYING 

upon  the  small  levels  attached  to  the  plate  of  the  transit 
and  perhaps  in  some  cases  to  the  horizontal  position  of  the 
plane  table.  For  each  foresight  and  for  each  backsight  the 
vertical  circle  should  be  set  at  zero;  the  telescope  is  then 
pointed  toward  the  rod,  the  tripod  head  screws,  in  the  case 
of  a  transit,  are  used  to  bring  the  telescope  level  and  then 
the  sight  is  taken.  The  accuracy  with  which  such  work  can 
be  done  with  a  transit  and  the  areas  that  can  be  covered  are 
surprising.  The  author  has  often  had  two  to  three  rodmen 
at  work  and  has  found  no  trouble  in  the  office  interpretation 
of  the  field  notes. 

The  method  of  occupying  with  the  instrument  only  the 
alternate  or  primary  stations  is  particularly  applicable  in 
making  surveys  of  reservoir  and  dam  sites,  in  taking  general 
topography  over  large  areas  and  in  securing  data  for  topo- 
graphic maps  of  mining  ground. 

The  foregoing  notes  relating  to  the  use  of  the  magnetic 
needle  in  topographic  surveying  were  written  with  special 
reference  to  surveys  made  with  a  transit.  They  are  with 
slight  modification  of  the  text  applicable  also  to  plane-table 
map  work. 

It  remains  to  be  said  that  a  magnetic  needle  5  ins.  long 
should  enable  the  field  work  to  be  done  with  about  the  same 
degree  of  accuracy  at  which  the  data  can  be  platted  on 
a  scale  of  about  200  ft.  to  the  inch  feVo)-  Longer  needles 
or  other  methods  of  work  should  be  used  when  maps  on  a 
very  large  scale  are  required  and  a  very  high  degree  of  accuracy 
is  demanded. 

Stadia  Notes.  It  has  already  been  stated  that  the  height 
at  the  instrument  station,  as  carried  into  the  notes,  if  the 
5-ft.  mark  be  selected  as  an  arbitrary  sighting-point,  is  a 
fictitious  height  5  ft.  lower  than  the  actual  height  of  the 
instrument.  It  often  happens  that  many  sights  can  be 
taken  without  noting  the  vertical  angle  by  using  the  transit 
as  a  level.  In  all  such  cases  the  level  foresight  as  made 
should  be  recorded,  but  this  rod-reading  should  not  be 


TOPOGRAPHIC  STADIA  SURVEYING  39 

applied  to  the  fictitous  station  height  used  in  calculating 
elevations  by  vertical  angle,  but  to  the  real  height  of  the 
instrument.  It  will,  therefore,  be  found  convenient  to  insert 
in  a  "  height  of  instrument  "  column  the  actual  height  of 
the  instrument  (the  fictitious  station  height  plus  5  ft.),  sub- 
tracting from  this,  as  in  leveling,  whenever  the  transit  is 
used  as  a  level. 

The  fictitious  transit  station  elevation,  it  will  be  noted, 
is  carried  forward  into  the  column  for  ground  heights  and  is 
identified  by  underlining.  To  this  transit  station  elevation 
all  differences  in  elevation,  as  determined  by  vertical  angles 
with  sights  to  the  5-ft.  mark,  are  applied  to  calculate  the 
ground  heights. 

When,  in  taking  a  foresight  or  a  sight  to  any  point  whose 
elevation  is  to  be  determined,  the  cross-hair  in  determining 
the  vertical  angle  is  set  on  some  foot  mark  n  other  than  the 
foot  mark  5,  then  subtract  (n— 5)  from  the  elevation. 

When  a  backsight  is  taken  to  any  mark  n  on  the  rod  other 
than  the  foot  mark  5  then  add  to  the  new  instrument  station 
height  (n-5)  ft. 

The  backsight  which  appears  in  the  notes  as  though  taken 
from  an  even  numbered  (secondary)  station  is,  in  fact,  the 
first  sight  taken  from  the  next  instrument  station.  The 
notes  thus  become  a  simple  combination  of  transit  and  level 
notes. 


40 


TOPOGRAPHIC  STADIA  SURVEYING 


NOTE-BOOK— 


LEFT-HAND  PAGE 


Rod 
Read- 
ing. 

Dis- 
tance. 

Magnetic 
Course. 

Vertical 
Angle. 

Difference  in 
Elevation. 

Back- 
sight. 

Height 
of  In- 
stru- 
ment. 

Level 
Sights, 
Pore- 
sight. 

Topog 

raphic  Su 

rvey  of 

The  Eagl 

e   Mine 

Oct.   17, 

1915 

Station 

0 

362 

342 

N27  15E 

+  13.21 

+81.  61 

Station 

1 

256 

257 

S31    35  W 

-2.52 

-12.8 

116 
371 

117 
372 

S80  SOW 
S83  25W 

-3.17 
-f-2  00 

-6.7 
+  13  0 

613 

603 

N45  OOW 

+8   14 

+87  0 

300 

288 

N36  10W 

+  12  05 

+61  7 

900 

831 

N3  15E 

+  16.09 

+240.8 

950 

883 

N20  30E 

+  15.30 

-2.0+245.0 

428 
730 

428 
717 

N85  OOE 
N60  10E 

+2.17 
+8  07 

+3.0+17.1 
+  102  23 

436 

437 

Station 
N40  15E 

2 

6   17 

327  43 

3 

327  43 

925 

926 

S6    45E 

8.3 

706 

707 

N35  05E 

3.16 

ooc 

331 

Station 
N62  30E 

4 
+9   11 

+53  48 

TOPOGRAPHIC  STADIA  SURVEYING 


41 


SAMPLE  PAGES 


RIGHT-HAND  PAGE 


Remarl 


Transit  No.  36. 
e  =  l.l5  ft. 

All  vertical  angle  sights  are  to  the  5-ft.  mark  on  the  rod  unless 
otherwise  noted. 

Odd-numbered  points  are  the  instrument  stations. 

Even-numbered  points  are  the  turning  points. 
U.  S.  G.  S.  Bench,  top  of  iron  pipe,  located,  etc. 

To  Station  1  gentle  slope  to  S. 


Bottom  of  gulch. 
Slope  to  SW. 
Bottom  of  gulch. 
Bottom  of  gulch. 
Slope  to  W. 
Top  of  bluff. 
To  7  ft.     Top  of  bluff. 
To  2  ft.     Slope  to  S. 
To  station  2. 


To  Station  3.  The  fictitious  (though  approximate)  elevation  of 
ground  at  Station  3,  and  Station  elevation  is  found  by  sub- 
tracting 5  ft.  from  the  H.  I. 


At  E.  edge  of  timber. 

To  Station  4.     Temporary  B.  M.,  etc. 


To  Station  5. 


42 


TOPOGRAPHIC  STADIA  SURVEYING 


NOTE-BOOK— 


Rod 
Read- 
ing. 

Dis- 
tance. 

Magnetic 
Course. 

Vertical 
Angle. 

Difference  in 
Elevation. 

Back- 
sight. 

Height 
of  In- 
stru- 
ment. 

Level 
Sights, 
Fore- 
sight. 

Station 

5 

382.75 

516 

511 

Nil  05W 

—6  18 

—56  4 

0 

0 

5.2 

437 

438 

N36  10W 

9.26 

Station 

6 

462 

461 

N20  OOE 

3  56 

+3  —31   09 

Station 

7 

620 

618 

N10  OOE 

+4   12 

+45  33 

417 

417 

N51  20E 

-3.06 

-22.57 

Station 

8A. 

516 

511 

N80  OOE 

+6.16 

+56.13 

Station 

8B. 

565 

538 

N31  45E 

+12.56 

+  123.51 

Station 

9 

Etc. 

TOPOGRAPHIC  STADIA  SURVEYING 


43 


SAMPLE  PAGES — Continued 


Eleva- 
tions. 


377.75 


321.4 
377.6 
373.49 

373.49 


344.80 


390.13 
322.23 


390.13 


446.26 
322.23 


Remarks. 


Ground  at  instrument. 
To  Station  6. 


To  8  ft.  to  Station  7. 


To  Station  8A. 
To  Station  8B. 


To  Station  9 


To  Station  9 


44  TOPOGRAPHIC  STADIA  SURVEYING 

Vertical  Angles  Measured  with  an  Alidade.  In  using 
the  alidade  of  the  plane-table  for  measuring  angles  in  a 
vertical  plane,  two  readings  on  the  vertical  circle  are  neces- 
sary. First,  the  index  error  when  the  telescope,  pointed 
toward  the  rod,  is  in  a  horizontal  position;  second,  the 
angle  when  the  telescope  is  depressed  or  elevated  toward 
the  sighting-point.  A  combination  of  the  two  readings 
gives  the  angle  of  depression  or  elevation.  It  would  be  a 
convenience  to  have  the  index  arranged  movable  and  pro- 
vided with  a  tangent  screw,  similar  to  the  lower  plate  of  the 
transit,  so  that  the  telescope  could  be  leveled  carrying 
with  it  the  index  set  at  zero.  Unclamping  and  sighting 
could  then  be  followed,  as  with  a  transit,  by  a  reading  of 
the  vertical  angle  freed  from  index  error.  The  index  error 
here  referred  to  is  due  to  the  fact  that  a  plane-table  is  not 
expected  to  have  a  perfectly  true  surface  and  cannot  be 
leveled  with  the  accuracy  desirable  in  measuring  vertical 
angles. 

The  Amount  of  Error  when  the  Sighting  Point  does  not 
Bisect  the  Intercept.  The  formulas  presented  in  this  manual 
are  based  on  the  assumption  that  the  portion  of  the  stadia  rod 
which  is  read  for  distance  is  bisected  by  the  middle  cross-hair 
when  the  vertical  angle  is  read.  As  a  matter  of  fact  this 
condition  rarely  obtains  in  practice.  The  lower  cross-hair 
is  set  upon  some  foot  mark  and  the  intercept  is  read  on  the 
upper  cross-hair,  thereupon  the  middle  cross-hair  is  set  upon 
the  sighting-point  and  the  rodman  is  waved  off. 

In  order  that  the  topographer  may  have  a  clear  concep- 
tion of  the  error  introduced  when  the  rod  is  read  for  distance, 
with  the  middle  cross-hair  at  some  point  on  the  rod  other 
than  the  sighting-point,  Tables  1  and  2  have  been  prepared. 
It  will  be  seen  from  these  that  for  small  vertical  angles  and 
sights  of  any  length,  very  little  attention  need  be  paid  to  the 
portion  of  the  rod  used  in  measuring  distance.  The  impor- 
tance of  having  the  middle  cross-hair  near  the  sighting-point 
when  reading  for  distance,  increases,  regardless  of  the  actual 


TOPOGRAPHIC  STADIA  SURVEYING 


45 


distance  to  the  rod,  as  the  angle  of  elevation  or  depression 
increases. 

TABLE  1 

TABLE  OF  CORRECTIONS  TO  BE  APPLIED  WHEN  THE 
ROD  IS  READ  WITH  THE  TELESCOPE  AT  A  VERTICAL 
ANGLE  OF  GREATER  AMPLITUDE  THAN  THE  RE- 
CORDED VERTICAL  ANGLE  (TO  THE  SIGHTING- 
POINT).  DECREASE  THE  DISTANCE  AND  DECREASE 
THE  DIFFERENCE  IN  ELEVATION  BY  THE  AMOUNTS 
NOTED  IN  THE  TABLE 


II 

•3.8  If 

Vert.  Angle 
=  1° 

Vert.  Angle 
=  5° 

Vert.  Angle 
=  10° 

Vert.  Angle 
=  20° 

Vert.  Angle 
=  30° 

bib 

Is* 

T3 

O  3  bo 

Corrections 

Corr  actions 

Corrections 

Corrections 

Corrections 

« 

§15 

Feet. 

Feet, 

Feet. 

Feet. 

Feet. 

P4 

^3  Oj_bB 

1 

|QGO 

Dist. 

Elev 

Dist. 

Elev. 

Dist. 

Elev. 

Dist. 

Elev. 

Dist. 

Elev. 

100 

1 

.04 

0 

.18 

.02 

.34 

.06 

.66 

.24 

.86 

.50 

100 

2 

.13 

0 

.41 

.04 

.70 

.13 

1.32 

.'48 

1.72 

1.00 

100 

3 

.23 

0 

.64 

.06 

1.07 

.20 

1.98 

.73 

2.58 

1.50 

100 

4 

.32 

0 

.87 

.08 

1.44 

.27 

2.65 

.97 

3.45 

2.00 

100 

5 

.42 

0 

1.11 

.10 

1.91 

.34 

3.32 

1.21 

4.32 

2.50 

200 

1 

.04 

0 

.2 

.02 

.3 

.05 

.6 

.20 

.9 

.50 

200 

2 

.10 

0 

.4 

.03 

.7 

.12 

1.3 

.45 

1.7 

1.00 

200 

3 

.17 

0 

.6 

.05 

1.1 

.18 

1.9 

.70 

2.6 

1.50 

200 

4 

.23 

0 

.8 

.07 

1.5 

.25 

2.6 

.95 

3.5 

2.00 

200 

5 

.30 

0 

1.0 

.09 

1.9 

.32 

3.3 

1.20 

4.3 

2.50 

500 

1 

.04 

0 

.2 

.02 

.3 

.05 

.6 

.23 

.9 

.45 

500 

2 

.08 

0 

.3 

.03 

.7 

.11 

1.2 

.46 

1.7 

.95 

500 

3 

.13 

0 

.5 

.05 

1.1 

.17 

1.9 

.70 

2.6 

1.45 

500 

4 

.18 

0 

.7 

.06 

1.5 

.23 

2.5 

.93 

3.4 

1.95 

500 

5 

.23 

0 

.9 

.08 

1.8 

.30 

3.2 

1.16 

4.3 

2.45 

1000 

1 

.03 

0 

.2 

.02 

.4 

.06 

.7 

.23 

.9 

.45 

1000 

2 

.07 

0 

.3 

.03 

.7 

.12 

1.3 

.46 

1.7 

.95 

1000 

3 

.11 

0 

.5 

.05 

1.0 

.18 

1.9 

.70 

2.6 

1.40 

1000 

4 

.15 

0 

.7 

.06 

1.3 

.24 

2.6 

.93 

3.4 

1.90 

1000 

5 

.20 

0 

.9 

.08 

1.7 

.30 

3.2 

1.16 

4.3 

2.40 

The  tables  are  prepared  as  correction  tables,  but  it  will  be 
well  to  remember  that  no  correction  is  necessary  if  the  rule 
be  observed  requiring  the  middle  cross-hair  to  be  first  placed 
on  the  sighting-point,  and  then  setting  the  lower  cross-hair 


46 


TOPOGRAPHIC  STADIA  SURVEYING 


upon  the  foot  mark  nearest  to  the  lowest  cross-hair.  The 
error  under  observance  of  this  rule  will  be  so  small  as  to  be 
negligible  in  all  surveys,  except  in  special  cases  where  the 
highest  attainable  accuracy  may  be  a  requirement. 

Whenever  the  bisecting  point  of  the  intercept  is  within 
one  foot  of  the  sighting-point  the  error  in  distance  for  any 
vertical  angle  less  than  30°  cannot  exceed  1  ft. 

TABLE  2 
TABLE  OF  CORRECTIONS  TO  BE  APPLIED  WHEN  THE 

ROD  IS  READ  WITH  THE  TELESCOPE  AS  A  VERTICAL 
ANGLE  OF  LESS  AMPLITUDE  THAN  THE  RECORDED 
VERTICAL  ANGLE  (TO  THE  SIGHTING-POINT).  IN- 
CREASE THE  DISTANCE  AND  INCREASE  THE  DIF- 
FERENCE IN  ELEVATION  BY  THE  AMOUNTS  NOTED 
IN  THE  TABLE 


ll 

Vert.  Anglr- 

Vert.  Anglo 

Vert.  Angle 

Vert.  Angle 

Vert.  Angle 

*-•  S 

=  1° 

=  5° 

=  10° 

=  20° 

=  30° 

3lf 

ob 

a 

is* 

«^  3  M 

Corrections 

Corrections 

Corrections 

Corrections 

Corrections 

s 

U-g.2 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Cd 

^  n.'rt 

^  o  &o 

0 

3Qo2 

ii 

Dist. 

Elev. 

Dist. 

Elev. 

Dist. 

Elev. 

Dist. 

Elev. 

Dist: 

Elev. 

100 

1 

.02 

0 

.16 

.01 

.33 

.05 

.63 

.22 

.87 

.50 

100 

2 

.03 

0 

.31 

.03 

.64 

.10 

1.25 

.44 

1.73 

1.00 

100 

3 

.02 

0 

.44 

.04 

.94 

.16 

1.85 

.66 

2.59 

1.50 

100 

4 

-.02 

0 

.54 

.05 

1.22 

.21 

2.44 

.88 

3.46 

1.95 

100 

5 

-.08 

0 

.62 

.05 

1.49 

.26 

3.07 

1.10 

4.32 

2.40 

200 

1 

.03 

0 

.2 

.01 

.3 

.06 

.6 

.22 

.9 

.50 

200 

2 

.05 

0 

.3 

.03 

.7 

.12 

1.2 

.45 

1.7 

1.00 

200 

3 

.06 

0 

.5 

.04 

1.0 

.17 

1.9 

.67 

2.6 

1.50 

200 

4 

.06 

0 

.6 

.05 

1.3 

.23 

2.6 

.89 

3.4 

1.95 

200 

5 

.05 

0 

.7 

.06 

1.6 

.28 

3.2 

1.12 

4.3 

2.40 

500 

1 

.03 

0 

.2 

.01 

.3 

.06 

.6 

.23 

.9 

.50 

500 

2 

.05 

0 

.3 

.03 

.7 

.12 

1.2 

.46 

1.7 

1.00 

500 

3 

.07 

0 

.5 

.04 

1.0 

.17 

1.9 

.68 

2.6 

1.50 

500 

4 

.09 

0 

.7 

.06 

1.3 

.23 

2.6 

.91 

3.4 

1.95 

500 

5 

.10 

0 

.8 

.07 

1.6 

.28 

3.2 

1.14 

4.3 

2.40 

1000 

1 

.03 

0 

.2 

.01 

.4 

.06 

.6 

.23 

.9 

.50 

1000 

2 

.06 

0 

.3 

.03 

.7 

.12 

1.3 

.46 

1.7 

1.00 

1000 

3 

.09 

0 

.5 

.04 

1.1 

.18 

1.9 

.70 

2.6 

1.50 

1000 

4 

.12 

0 

.7 

.06 

1.4 

.24 

2.6 

.93 

3.4 

1.95 

1000 

5 

.15 

0 

.8 

.07 

1.7 

.30 

3.2 

1.16 

4.3 

2.40 

TOPOGRAPHIC  STADIA  SURVEYING  47 

The  columns  in  the  tables  bearing  the  heading  "  Middle 
hair  departures  from  the  sighting-point  "  contain  the  depart- 
ure of  the  bisecting  point  of  the  intercept  from  the  sighting- 
point  for  which  the  corrections  in  the  succeeding  columns 
have  been  computed. 

The  sighting  can,  as  stated,  always  be  done  in  such  manner 
that  the  use  of  these  tables  will  not  be  necessary.  Their 
introduction  is  mainly  for  the  purpose  of  showing  the  errors 
that  will  result  if  proper  attention  be  not  paid  to  the  part 
of  the  rod  read  for  distance. 

Amount  of  Error  Due  to  Inclined  Rod.  If  the  stadia 
rod  be  not  held  in  a  true  vertical  position,  or  if,  in  the  case 
of  a  sectional  rod  the  face  of  the  rod  is  in  two  or  more  planes, 
appreciable  error  may  result.  All  such  error  should  be 
avoided.  Nevertheless  in  order  that  the  magnitude  thereof 
may  not  be  underestimated  attention  is  called  to  the  following 
facts. 

Let  it  be  supposed  that  a  rod  is  built  up  of  two  sections  of 
which  the  uppermost  is  fastened  to  the  back  of  the  lower  one 
and  that  the  thickness  of  the  lower  section  and,  therefore, 
the  departure  of  the  upper  section  from  the  plane  of  the  lower 
one  is  |  of  an  inch  or  .0875  ft. 

If  now  a  reading  for  distance  is  made  on  this  rod  with  one 
cross-hair  on  the  lower  and  one  on  the  upper  section  the 
resulting  error  in  distance  will  be : 

For  vertical  angle  +  5°  rod  reading  too  small  by  0.8  ft. 
For  vertical  angle  +10°  rod  reading  too  small  by  1.5  ft. 
For  vertical  angle  +20°  rod  reading  too  small  by  3.2  ft. 
For  vertical  angle  +30°  rod  reading  too  small  by  5.0  ft. 
For  vertical  angle  —  5°  rod  reading  too  large  by  0.8  ft. 
For  vertical  angle  —10°  rod  reading  too  large  by  1.5  ft. 
For  vertical  angle  —20°  rod  reading  too  large  by  3.2  ft. 
For  vertical  angle  —30°  rod  reading  too  large  by  5.0  ft. 

It  is  to  be  noted  that  in  the  case  of  short  sights  the  per- 
centage of  error  when  sighting  up  or  down  will  be  relatively 


48  TOPOGRAPHIC  STADIA  SURVEYING 

high.  The  amount  of  this  error  is  independent  of  the  dis- 
tance, being  dependent  solely  upon  the  vertical  angle  of  the 
sight  and  the  departure  of  the  surface  on  which  one  cross- 
hair is  read  from  that  on  which  the  other  is  read. 

When  due  to  carelessness  or  any  other  cause  the  stadia 
rod  is  inclined  forward  or  backward,  and  departs  from  a 
true  vertical  plane,  the  error  will  be  as  shown  in  Tables  3 
and  4. 

The  Accuracy  of  Telemeter  Surveys.  The  accuracy 
of  the  survey  made  with  the  telemeter  and  stadia  rod  is  not 
readily  determinable.  The  error  in  single  readings  may 
vary  within  considerable  limits.  The  reading  is  affected 
not  alone  by  the  care  with  which  the  telemeter  and  the  rod 
have  been  constructed,  but  also  by  atmospheric  and  light 
conditions  and  by  the  personal  equation  of  the  observer. 

Under  fair  conditions  the  individual  readings,  when  the 
distances  do  not  exceed  800  ft.  should  have  a  probable  error 
less  than  1  in  500.  When  a  survey  is  under  consideration 
made  up  of  a  number  of  courses,  aggregating  about  a  mile 
in  length,  the  error  with  ordinary  care  and  with  instruments 
suitable  for  ordinary  good  work,  should  not  exceed  1  in 
1000.  When  a  still  longer  distance  is  measured  by  many 
sights,  each  less  than  800  ft.,  the  probable  error  will  be  less 
than  this  amount.  According  to  the  law  of  least  squares, 
possibly  1  in  2000  when  the  aggregate  length  of  the  survey  is 
about  4  miles. 

In  view  of  the  relatively  large  possible  error  in  a  single 
sight,  it  would  be  useless  to  note  distances  other  than  to 
the  nearest  foot,  when  ordinary  topographic  surveys  are 
involved.  Elevations  of  temporary  reference  points,  such 
as  turning-points  and  of  permanent  bench  marks,  should  be 
entered  in  the  notes  to  hundredths.  The  height  of  instru- 
ment, too,  should  be  entered  to  hundredths  of  a  foot.  The 
elevation  of  the  ground  at  any  point  and  the  differences  in 
elevation  for  use  in  determining  ground  heights  should  be 
noted  to  tenths  only. 


TOPOGRAPHIC  STADIA  SURVEYING 


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TOPOGRAPHIC   STADIA   SURVEYING  51 

The  Effect  of  Refraction.  As  is  well  known  the  refraction 
of  light  rays  is  a  function  of  the  unequal  density  of  the 
atmosphere.  Near  the  ground  surface,  at  times  when  there 
is  material  difference  in  the  temperature  of  the  air  and  of  the 
ground,  there  may  be  a  material  variation  in  the  refraction 
with  but  a  few  feet  difference  in  the  elevation  of  the  light 
ray.  The  refraction  will  in  other  words  be  different  for  the 
light  rays  from  the  lower  and  upper  portions  of  a  telemeter 
rod.  This  fact  and  its  influence  upon  the  measurement  of 
distances  by  means  of  a  telescope  and  stadia  rod  has  been 
ably  discussed  by  Mr.  L.  S.  Smith,  C.  E.,*  and  need  not  be 
dwelt  upon  here.  It  will  suffice  to  say  that  the  refraction 
effect  Upon  the  rod-readings  is  greatest  at  midday  and  is  not 
the  same  on  different  days.  The  rating  and  testing  of  the 
telemeter  should,  therefore,  be  extended  over  a  number  of 
days  and  should  include  observations  in  the  morning  and 
evening  as  well  as  at  midday. 

Instances  have  been  found  where,  in  dry,  arid  regions  such 
as  Arizona,  the  errors  due  to  refraction  have  been  so  great 
that  the  use  of  the  ordinary  stadia  rod  has  had  to  be  aban- 
doned for  accurate  work.  In  such  instances,  the  use  of  a 
horizontal  rod  with  a  special  supporting  device  can  be  rec- 
ommended. 

*  University  of  Wisconsin  Bulletin,  Engineering  Series,  Vol.  1, 
No.  5. 


CHAPTER  VII 
THE  PLATTING  OF  STADIA  NOTES 

WHEN  topographic  surveys  are  made  with  a  transit  the 
field  observations — except  foresights  and  backsights — are 
usually  reduced  in  the  office,  where,  too,  the  notes  are  platted. 

In  order  that  the  work  may  readily  be  manifolded  the  aim 
is  to  secure  an  inked  copy  on  tracing  linen  or  other  trans- 
parent material  with  the  least  degree  of  labor. 

The  following  procedure  can  be  recommended: 

Use  an  open  protractor  of  thin  material,  such  as  paper, 
with  radius  equal  to  or  greater  than  the  lengths  of  the  sights 
to  be  platted.  Make  the  pencil  drawing  upon  the  rough  side 
of  tracing  linen  or  upon  tracing  paper  placed  over  cross-section 
or  profile  paper.  The  closely  spaced  parallel  lines  visible 
through  the  tracing  linen  are  an  invaluable  aid  in  the  quick 
orientation  of  the  protractor  whenever  the  azimuths  are 
referred  to  the  north  line  or  whenever  they  are  given  in  the 
relation  to  the  cardinal  points  of  the  compass. 

By  placing  a  scale,  or  a  marked  ruler,  or  a  strip  of  paper, 
north  and  south  or  east  and  west  across  the  protractor,  the 
same  can  be  conveniently  centered  and  oriented  at  one 
operation.  No  lines  from  instrument  station  to  topographic 
points  should  be  drawn.  The  only  survey  lines  to  appear  on 
the  drawing  are  those  of  the  traverse  from  station  to  station. 
A  fine  needle  at  the  instrument  station  from  which  the  sights 
are  being  platted  is  a  convenience  and  will  decrease  the  lia- 
bility of  making  errors  in  platting.  Special  scales  with  zero 
point  swinging  upon  this  needle  and  other  devices  to  simplify 
the  office  work  readily  suggest  themselves. 

52 


TOPOGRAPHIC  STADIA  SURVEYING  53 

After  the  pencil  drawing  has  been  made  and  corrected  to 
fit  the  controlling  points  of  the  survey,  a  fresh  sheet  of 
tracing  linen  is  used  upon  which  to  ink  the  finished  map. 
This  is  then  available  for  any  of  the  ordinary  processes  of 
manifolding,  such  as  blue  or  black  printing,  photolithograph- 
ing,  etc. 


CHAPTER  VIII 
TABLES 


A  NUMBER  of  tables  are  here  presented  which  the  sur- 
veyor who  uses  his  transit  as  a  telemeter  or  who  makes 
topographic  surveys  with  the  plane  table  will  find  useful. 

Table  5  gives  the  values  of  the  terms  e  cos  a  and  e  sin  a 
which  appear  in  the  correct  stadia  formulas  (17)  and  (18) 
and  covers  all  ordinary  values  of  e.  For  each  instrument, 
there  being  but  one  value  of  e,  only  a  single  line  of  the  table 
will  apply.  This  particular  line  should  be  made  the  basis 
of  a  secondary  table  for  the  topographer's  own  instrument, 
giving  the  values  for  each  degree  so  that  interpolation  will  be 
simplified. 

TABLE  5 

VALUES  OF  e  cos  a  AND  e  sin  a  FOR  DIFFERENT  VALUES 
OF  INSTRUMENT  CONSTANT  e  AND  DIFFERENT 
ANGLES  OF  ELEVATION  a 

All  values  in  feet 


1 

5 

o 

1C 

11 

>° 

2C 

3 

Values 

of  e 

e  cos 

e  sin 

e  cos 

e  sin 

e  cos 

e  sin 

e  cos 

e  sin 

e  cos 

e  sin 

e  cos 

e  sin 

0.80 

0.80 

.01 

.80 

.07 

.79 

.14 

.77 

.21 

.75 

.27 

.69 

.40 

1.00 

1.00 

.02 

1.00 

.09 

.98 

.17 

.97 

.26 

.94 

.34 

.87 

.50 

1.20 

1.20 

.02 

1.19 

.10 

.18 

.21 

1.16 

.31 

1.13 

.41 

1.04 

.60 

1.40 

1.40 

.03 

1.39 

.12 

.38 

.24 

1.35 

.36 

1.32 

.48 

1.21 

.70 

1.60 

1.60 

.03 

1.59 

.14 

.57 

.28 

1.54 

.41 

1.50 

.55 

1.39 

.80 

1.80 

1.80 

03 

1.79 

.16 

.77 

.31 

1.74 

.47 

1.69 

.62 

1  .  56 

.90 

2.00 

2.00 

.03 

1.99 

.17 

.97 

.35 

1.93 

.52 

1.88 

.68 

1.73 

1.00 

2.50 

2.50 

.04 

2.49 

.22 

2.  40 

.43 

2.41 

.65 

2.35 

.85 

2.16 

1.25 

54 


TOPOGRAPHIC  .STADIA  SURVEYING  55 


STADIA  REDUCTION  TABLE 

Table  6  is  a  stadia  reduction  table,  checked  by  Mr.  Otto 
von  Geldern,  to  facilitate  the  solution  of  the  equations. 

D=r  cos"  a+e  cos  a;       ....     (17) 

h  =r  sin  a  cos  a+e  sin  «;        .     .     .(18) 
or 

sin  2« 
h=r — He  sin  « (19) 

The  tables  as  here  published  contain  only  the  increments 

100  cos?  a    and     100  sin  a  cos  a, 
In  using  formulas  (17)  and  (18)  the  values  taken  from  the 

tables  are  to  be  multiplied  by   -— .     In  determining  dis- 

luu 

tance  e  cos  a  and  in  determining  difference  in  elevation 
e  sin  a  are  then  to  be  added  to  the  values  found  in  the  tables. 
In  illustrating  the  use  of  these  tables  Mr.  von  Geldern  uses 
the  following  figures: 

For  a  rod-reading  r=285  ft.  and  a  vertical  angle  10°  12' 
there  will  be  found  in  the  table  in  the  column  "  Hor.  Dist." 
96.86  and  in  the  column  "'Diff.  Elev."  17.43;  in  other  words 

100  cos2  (10°  12')  =96.86  ft., 
and 

100  sin  (10°  12')  .IPS  (10°  12')  =17.43  ft. 


2jUos( 
to  bo  mi 


285 
Both  of  these  values  are  to  ^multiplied  by  ^-^  =2.85. 

J.  \)\) 

Therefore 

285  cos2  (10°  12')  =2.85x96.86=276.05; 

285  sin  (10°  12')  cos  (10°  12')  =2.85x17.43=49.67. 


56  TOPOGRAPHIC  STADIA  SURVEYING 

If  a  large  ordinary  transit  has  been  used  the  value  of  e  will 
be  about  1.15  ft.,  and  therefore 

1.15  cos  (10°  120=1.13; 
and 

1.15  sin  (10°  120=0.21, 
consequently 

D  =276.05+1.  13  =277.18; 

A  =49.67  +0.21  =49.88. 

The  chief  value  of  Table  6  lies  in  the  fact  that  it  is  applica- 
ble to  the  solution  of  the  approximation  formulas  which  are 
recommended  in  this  manual  for  use  in  stadia  surveying. 
Thus  in  the  case  of 


(27)  Z) 
and 

(28)  h  =  (r  +e)  sin  a  cos  a. 

For  the  special  case  (r+e)  =285  +  1.15=286.15; 

286  15 
D  =-  X96.86  =277.16  ft.; 


h=-X  17.43  =49.88  ft. 
Again  in  the  case  of 


(29)  D  =  (r  +  l)  cos2  «; 

(30)  A  =  (r  +  l)  sin  a  cos  a. 
For  the  special  case  of  (r  +  1)  =286; 

286 
D=X96.86  =277.02  ft.; 


286 

™X  17.43  =49.85  ft. 

1UU 


TOPOGRAPHIC  STADIA  SURVEYING 


57 


TABLE  6 

STADIA  REDUCTION  TABLE 
For  instruments  rated  1  to  100 

In  the  column  "  Hor.  Dist."  find:    100  cos2  a 
In  the  column  "  Diff.  Elev."  find:    100  sin  a  cos  a 
Rod  Vertical 


Min. 

0° 

1 

2 

3 

4° 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

0 

100.00        .00 

P3.97       1.74 

99.88       3.49 

99.73       5.23 

99.51       6.96 

2 

100.00        .00 

09.97       1.80 

99.87       3.55 

99.72       5.28 

99.51       7.C2 

4 

100.00        .12 

£).97       1.86 

99  .  87       3  .  60 

99.71       5.34 

99.50       7.07 

G 

100.00        .17 

39.96       1.92 

99.87       3.6C 

99.71       5.40 

99.49       7.13 

8 

100.00        .23 

99.96       1.98 

39.86       3.72 

99.70       5.46 

99.48       7.19 

10 

100.00        .29 

99.96       2.04 

99  .86       3  .  78 

99-69       5.52 

99.47       7.25 

12 

100.00        .35 

99.96       2.09 

99.85       3.84 

99.69       5.57 

99.46       7.30 

14 

100.00        .41 

99.95       2.15 

39.85       3.90 

99.68       5.63 

99.46       7.36 

16 

100.00        .47 

99.95        2.21 

99.84       3.95 

99.68       5.69 

99.45       7.42 

18 

100.00        .52 

39.95       2.27 

99.84       4.01 

99.67       5.75 

99.44       7.48 

20 

100.00        .58 

39  .  95        2  .  33 

99.83       4.07 

99.66       5.80 

99.43       7.53 

22 

100.00        .64 

99.94       2.38 

99.83       4.13 

99.66       5.86 

99.42       7.59 

24 

100.00        .70 

99.94        2.44 

39.82       4.18 

99.65       5.92 

99.41       7.65 

26 

99.99        .76 

99.94       2.50 

39.82       4.24 

99.64       5.98 

99.40       7.71 

28 

99.99        .81 

99.93       2.56 

99.81        4.30 

99.63       6.04 

99.39       7.76 

30 

99.99        .87 

99.93        2.62 

99.81        4.36 

99.63       6.09 

99.38       7.82 

32 

99.99        .93 

99.93       2.67 

99.80       4.42 

99.62       6.15 

99.38       7.88 

34 

99.99        .99 

99.93       2.73 

99.80       4.48 

99.62       6.21 

99.37       7.94 

36 

99.99        .05 

99.92       2.79 

99  .  79       4  .  53 

99.61       6.27 

99.36       7.99 

38 

99.99        .11 

99.92       2.85 

99.79       4.59 

99.60       6.33 

99.35       8.05 

40 

99.99        .16 

99.92       2.91 

99.78       4.65 

99.59       6.38 

99.34       8.11 

42 

99.98        .22 

99.91       2.97 

39.78       4.71 

99.59       6.44 

99.33       8.17 

44 

99.98        .28 

99.91       3.02 

39.77       4.  76 

99.58       6.50 

99.32       8.22 

46 

99.98        .34 

99.90       3.08 

99.77       4.8£ 

99.57       6.56 

99.31       8.28 

48 

99.98     1.40 

99.90       3.14 

39.76       4.88 

99.56       6.61 

99.30       8.34 

50 

99.98     1.45 

99.90       3.20 

99.76       4.94 

99  .  56       6  .  67 

99  .  29       8  .  40 

52 

99.98     1.51 

99.89       3.26 

99.75       4.99 

99.55       6.73 

99.28       8.45 

54 

99.98     1.57 

39.89       3.31 

39.74       5.05 

99.54       6.78 

99.27       8.51 

56 

99.97     1.63 

99  .  89       3  .  37 

99.74       5.11 

99.53       6.84 

99.26       8.57 

58 

99.97     1.69 

39.88       3.43 

99.73       5.17 

99.52       6.90 

99.25       8.63 

60 

99.97     1.7499.88       3.49 

99.73       5.23 

99.51       6.96 

99.24       8.68 

58 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  6. — Continued 

STADIA  REDUCTION  TABLE 

For  instruments  rated  1  to  100 

In  the  column  "  Hor.  Dist."  find:    100  cos2  a 
In  the  column  "  Diff.  Elev."  find:    100  sin  a  cos  a 
Rod  Vertical 


Min. 

5° 

6° 

7° 

8° 

9° 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

Hor.       Diff. 
Dist.       Elev. 

Hor.       Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

0 

99.24       8.68 

98.91     10.40 

98.51     12.10 

98.06     13.78 

97.55     15.45 

2 

99.23       8.74 

98.90     10.45 

98.50     12.15 

98.05     13.84 

97.53     15.51 

4 

99.22       8.80 

98.88     10.51 

98.48     12.21 

98.03     13.89 

97.52     15.56 

6 

99.21       8.85 

98.87     10.57 

98.47     12.26 

98.01     13.95 

97.50     15.62 

8 

99.20       8.91 

98.86     10.62 

98.46     12.32 

98.00     14.01 

97.48     15.67 

10 

99.19       8.97 

98.85     10.68 

98.44     12.38 

97.98     14.06 

97.46     15.73 

12 

99.18       9.03 

98.83     10.74 

98.43     12.43 

97.97     14.12 

97.44     15.78 

14 

99.17       9.08 

98.82     10.79 

98.41     12.49 

97.95     14.17 

97.43     15.84 

16 

99.16       9.14 

98.81     10.85 

98.40     12.55 

97.93     14.23 

97.41      15.89 

18 

99.15       9.20 

98.80     10.91 

98.39     12.60 

97.92     14.28 

97.39     15.95 

20 

99.14       9.25 

98.78     10.96 

98.37     12.66 

97.90     14.34 

97.37     16.00 

20 

99.13       9.31 

98.77     11.02 

98.36     12.72 

97.88     14.40 

97.35     16.06 

22 

99.11       9.37 

98.76     11.08 

98.34     12.77 

97.87     14.45 

97.33     16.11 

24 

99.10       9.43 

98.74     11.13 

98.33     12.83 

97.85     14.51 

97.31     16.17 

26 

99.09       9.48 

98.73     11.19 

98.31     12.88 

97.83     14.56 

97.29  "  16.22 

28 

99.08       9.54 

98.72     11.25 

98.29     12.94 

97.82     14.62 

97.28     16.28 

30 

99.07       9.60 

98.71     11.30 

98.28     13.00 

97.80     14.67 

97.26     16.33 

32 

99.06       9.65 

98.69     11.36 

98.27     13.05 

97.78     14.73 

97.24     16.39 

36 

99.05       9.71 

98.68     11.42 

98.25     13.11 

97.76     14.79 

97.22     16.44 

38 

99.64       9.77 

98.67     11.47 

98.24     13.17 

97.75     14.84 

97.20     16.50 

40 

99.03       9.83 

98.65     11.53 

98.22     13.22 

97.73     14.90 

97.18     16.55 

42 

99.01       9.88 

98.64     11.59 

98.20     13.28 

97.71     14.95 

97.16     16.61 

44 

99.00       9.94 

98.63     11.64 

98.19     13.33 

97.69     15.01 

97.14     16.66 

46 

98.99     10.00 

98.61     11.70 

98.17     13.39 

97.68     15.06 

97.12     16.72 

48 

98.98     10.05 

98.60     11.76 

98.16     13.45 

97.66     15.12 

97.10     16.77 

50 

98.97     10.11 

98.58     11.81 

98.14     13.50 

97.64     15.17 

97.08     16.83 

52 

98.96     10.17 

98.57     11.87 

98.13     13.56 

97.62     15.23 

97.06     16.88 

54 

98.94     10.22 

98.56     11.93 

98.11     13.61 

97.61     15.28 

97.04     16.94 

56 

98.93     10.28 

98.54     11.98 

98.10     13.67 

97.59     15.34 

97.02     16.99 

58 
60 

98.92     10.34 
98.91     10.40 

98.53     12.04 
98.51     12.10 

98.08     13.72 
98.06     13.  78 

97.57     15.40 
97.55     15.45 

97.00     17.05 
96.98     17.10 

TOPOGRAPHIC  STADIA  SURVEYING 


59 


TABLE  6. — Continued 
STADIA  .REDUCTION  STABLE 

For  instruments  rated  1  to  100 
In  the  column  "  Hor.  Dist."  find:    100  cos2  a 
In  the  column  "  Diff.  Elev."  find:    100  sin  a  cos  a 
Rod  Vertical 


Min. 

10° 

11° 

12° 

13° 

14° 

Hor.       Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

Hor.       Diff. 
Dist.       Elev. 

rlor.        Diff. 
Dist.       Elev. 

0 

96.98     17.10 

96.36     18.73 

95.68     20.34 

94.94     21.92 

94.15     23.47 

2 

96.96     17.16 

96.34     18.78 

95.65     20.39 

94.91     21.97 

94.12     23.52 

4 

96.94     17.21 

96.32     18.84 

95.63     20.44 

94.89     22.02 

94  .09     23  .  58 

6 

96.92     17.26 

96.29     18.89 

95.61     20.50 

94.86     22.08 

94.07     23.63 

8 

96.90     17.32 

96.27     19.85 

95.58     20.55 

94.84     22.13 

94.04     23.68 

10 

96.88     17.37 

96.25     19.00 

95.56     20.60 

94.81     22.18 

94.01     23.73 

12 

96.86     17.43 

96.23     19.05 

95.53     20.66 

94.79     22.23 

93.98     23.78 

14 

96.84     17.48 

96.21     19.11 

95.51     20.71 

94.77     22.28 

93.95     23.83 

16 

96.82     17.54 

96.18     19.16 

95.49     20.76 

94.73     22.34 

93.93     23.88 

18 

96.80     17.59 

96.16     19.21 

95.46     20.81 

94.71     22.39 

93.90     23.93 

29 

96.78     17.65 

96.14     19.27 

95.44     20.87 

94.68     22.44 

93.87     23.99 

22 

96.76     17.70 

96.12     19.32 

95.41     20.92 

94.66     22.49 

93.84     24.04 

24 

96.74     17.76 

96.09     19.38 

95.39     20.97 

94.63     22.54 

93.81     24.09 

26 

96.72     17.81 

96.07     19.43 

95.36     21.03 

94  .60     22  .  60 

93.79     24.14 

28 

96.70     17.86 

96.05     19.48 

95.34     21.08 

94  .58     22  .  65 

93.76     24.19 

30 

96.68     17.92 

36.03     19.54 

95.32     21.13 

94.55     22.70 

93.73     24.24 

32 

96.66     17.97 

96.00     19.59 

95.29     21.18 

94.52     22.75 

93.70     24.29 

34 

96.64     18.03 

35.98     19.64 

95.27     21.24 

94.50     22.80 

93  .67     24  .  34 

36 

96.62     18.08 

35.96     19.70 

95.24     21.29 

94  .47     22  .  85 

93.65     24.39 

38 

96.60     18.14 

95.93     19.75 

95.22     21.34 

94.44     22.91 

93.62     24.44 

40 

96.57     18.19 

35.91     19.80 

95.19     21.39 

94.42     22.96 

93.59     24.49 

42 

96.55     18.24 

95.89     19.86 

95.17     21.45 

94.39     23.01 

93.56     24.55 

44 

96.53     18.30 

95.86     19.91 

95.14     21.50 

94.36     23.06 

93.53     24.60 

46 

96.51     18.35 

95.84     19.96 

95.12     21.55 

94.34     23.11 

93.50     24.65 

48 

96.49     18.41 

95.82     20.02 

95.09     21.60 

94.31     23.  1C 

93.47     24.70 

50 

96.47     18.46 

95.79     20.07 

95.07     21.60 

94  .28     23  .  22 

93.45     24.75 

52 

96.45     18.51 

35.77     20.12 

35.04     21.71 

34.26     23.27 

93  ..42     24  .  80 

51 

96.42     18:57 

35.75     20.18 

35.02     21.76 

94.23     23.3: 

33.39     24.85 

56 

96.40     18.62 

35.72     20.22 

34.99     21.81 

94  .20     23  .  37 

33..  36     24.90 

58 

36.38     18.68 

35.70     20.28 

)4.97     21.87 

34.17     23.41 

33.33     24.95 

60 

96.36     18.73 

35.68     20.34 

)4.94     21.92 

34.15     23.47 

33.30     25.00 

60 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  6 — Continued 
STADIA  REDUCTION  TABLE] 

^  For  instruments  rated  1  to  100 
In  the  column  "  Hor.  Dist."  find    100  cos2  a 
In  the  column  "  Diff.  Elev."  find:    100  sin  a  cos  a 
Rod  Vertical 


Min. 

15° 

16° 

17° 

18° 

19° 

Hor.       Diff. 
Dist.      Elev. 

Hor.       Diff. 
Dist.       Elev. 

Hor.       Diff. 
Dist.      Elev. 

Hor.       Diff. 
Dist.      Elev. 

Hor.        Diff. 
Dist.       Elev. 

0 

93.30     25.00 

92.40     26.50 

91.45     27.96 

90.45     29.39 

89.40     30.78 

2 

93.27     25.05 

92.37     26.55 

91.42     28.01 

90.42     29.44 

89.36     30.83 

4 

93.24     25.10 

92.34     26.59 

91.39     28.06 

90.38     29.48 

89.33     30.87 

6 

93.21     25.15 

92.31     26.64 

91.35     28.10 

90.35     29.53 

89.29     30.92 

8 

93.18     25.20 

92.28     26.68 

91.32     28.15 

90.31     29.58 

89.26     30.97 

10 

93.10     25.25 

92.25     26.74 

91.29     28.20 

90.28     29.62 

89.22     31.01 

12 

93.13     25.30 

92.22     26.79 

91.26     28.25 

90.24     29.67 

89.18     31.06 

14 

93.10     25.35 

92.19     26.84 

91.22     28.30 

90.21     29.72 

89.15     31.10 

16 

93.07     25.40 

92.15     26.89 

91.19     28.34 

90.18     29.76 

89.11     31.15 

18 

93.04     25.45 

92.12     26.94 

91.16     28.39 

90.14     29.81 

89.08     31.19 

20 

93.01     25.50 

92.09     26.99 

91.12     28.44 

90.11     29.86 

89.04     31.24 

22 

92.98     25.55 

92  .06     27  .  04 

91.09     28.49 

90.07     29.90 

89.00     31.28 

24 

92.95     25.60 

92.03     27.09 

91.06     28.54 

90.04     29.95 

88.96     31.33 

26 

92.92     25.65 

92.00     27.13 

91.02     28.  ££ 

90.00     30.00 

88.93     31.38 

28 

92.89     25.70 

91.97     27.18 

90.99     28.63 

89.97     30.04 

88.89     31.42 

30 

92.86     25.75 

91.93     27.23 

90.96     28.68 

89.93     30.09 

88.86     31.47 

32 

92.83     25.80 

91.90     27.28 

90.92     28.73 

89.90     30.14 

88.82     31.51 

34 

92.80     25.85 

91.87     27.  ?3 

90.89     28.77 

89.86     30.19 

88.78     31.56 

36 

92.77     25.90 

91.84     27.38 

90.86     28.82 

89.83     30.23 

88.75     31.60 

38 

92.74     25.95 

91.81     27.43 

90.82     28.87 

89.79     30.28 

88.71     31.65 

40 

92.71     26.00 

91.77     27.48 

90.79     28.92 

89.76     30.32 

88.67     31.69 

42 

92.68     26.05 

91.74     27.52 

90.76     28.96 

89.72     30.37 

88.64     31.74 

44 

92.65     26.10 

91.71     27.57 

9Q.72     29.01 

89.69     30.41 

88.60     31.78 

46 

92.62     26.15 

91.68     27.62 

90.69     29.06 

89.65     30.46 

88.56     31.83 

48 

92.59     26.20 

91.65     27.67 

90.66     29.11 

89.61     30.51 

88.53     31.87 

50 

92.56     26.25 

91.61     27.72 

90.62     29.15 

89.58     30.55 

88.49     31.92 

52 

92.53     26.30 

91.58     27.77 

90.59     29.20 

89.54     30.60 

88.45     31.96 

54 

92.49     26.35 

91.55     27.81 

90.55     29.25 

89.51      30.65 

88.41     32.01 

56 

92.46     26.40 

91.52     27.86 

90  .52     29  .  30 

89.47     30.69 

88.38     32.05 

58 

92.43    '26.45 

91.48     27.91 

90.48     29.34 

89.44     30.74 

88.34     32.09 

60 

92.40     26.50 

91.45     27.96 

90.45     29.39 

89.40     30.78 

88.30     32.14 

TOPOGRAPHIC  STADIA  SURVEYING 


61 


TABLE  6 — Continued 
STADIA  REDUCTION  TABLE 

For  instruments  rated  1  to  100 
In. the  column  "  Hor.  Dist."  find:    100  cos2  a 
In  the  column  "  Diff.  Elev."  find:    100  sin  a  cos 
Rod  Vertical 


Min. 

20° 

21° 

22° 

23° 

24° 

Hor.        Diff. 
Dist.       Elev. 

Hor.        Diff. 
Dist.       Elev. 

:ior.        Diff. 
Dist.       Elev. 

Hor.        Diff. 

Dist.      Elev. 

Hor.        Diff. 
Dist.      Elev. 

0 

88.30     32.14 

87.16     33.46 

85.97     34.73 

84.73     35.97 

83.46     37.16 

2 

88.26     32.18 

87.12     33.50 

85.93     34.77 

84.69     36.01 

83.41     37.20 

1 

88.2*     32.23 

87.08     33.54 

85.89     34.82 

84.65     36.05 

83.37     37.23 

G 

88.1-3     32.27 

87.04     33.59 

85.85     34.86 

84.61     36.09 

83.33     37.27 

8 

88.15     32.32 

87.00     33.63 

85.80     34.90 

84.57     36.13 

83.28     37.31 

13 

88.11     32.36 

86.96     33.67 

85,76     34.94 

84.52     36.17 

83.24     37.35 

12 

88.08     32.41 

86.92     33.72 

85.72     34.98 

84.48     36.21 

83.20     37.39 

14 

88.04     32.45 

36.88     33.76 

85.68     35.02 

84.44     36.25 

83.15     37.43 

16 

88.00     32.49 

86.84     33.80 

85.64     35.07 

84.40     36.29 

83.11     37.47 

18 

87.96     32.54 

86.80     33.84 

85.60     35.11 

84.35     36.33 

83.07     37.51 

20 

87.93     32.58 

86.77     33.89 

85.56     35.15 

84.31     36.37 

83.02     37.54 

22 

87.89     32.63 

86.73     33.93 

85.52     35.19 

84.27     36.41 

82.98     37.58 

24 

87.85     32.67 

86.69     33.97 

85.48     35.23 

84.23     36.45 

82.93     37.62 

26 

87.81      32.72 

86.65     34.01 

85.44     35.27 

84.18     36.49 

82.89     37.66 

28 

87.77     32.76 

86.61     34.06 

85.40     35.31 

84.14     36.53 

82.85     37.70 

30 

87.74     32.80 

86.57     34.10 

85.36     35.36 

84.10     36.57 

82.80     37.74 

32 

87.70     32.85 

86.53     34.14 

85.31     35.40 

84.06     36.61 

82.76     37.77 

34 

87.66     32.89 

86.49     34.18 

85.27     35.44 

84.01     36.65 

82.72     37.81 

36 

87.62     32.93 

86.45     34.23 

85.23     35.48 

83.97     36.69 

82.67     37.85 

38 

87.58     32.98 

86.41     34.27 

85.19     35.52 

83.93     36.73 

82.63     37.89 

40 

87.54     33.02 

86.37     34.31 

85.15     35.56 

83.89     36.77 

82.58     37.93 

42 

87.51     33.07 

86.33     34.35 

85.11     35.60 

83.84     36.80 

82.54     37.96 

44 

87.47     33.11 

86.29     34.40 

85.07     35.64 

83.80     36.84 

82.49     38.00 

46 

87.43     33.15 

86.25     34.44 

85.02     35.68 

83.76     36.88 

82.45     38.04 

48 

87  .39     33  .  20 

86.21     34.48 

84.98     35.72 

83.72     36.92 

82.41     38.08 

50 

87.35     33.24 

86.17     34.52 

84.94     35.76 

83.67     36.96 

82.36     38.11 

52 

87.31     33.28 

86.13     34.57 

84.90     35.80 

83.63     37.00 

82.32     38.15 

54 

87.27     33.33 

86.09     34.61 

84.86     35.85 

83.59     37.04 

82.27     38.19 

56 

87.24     33.37 

86.05     34.65 

84.82     35.89 

83.54     37.08 

82.23     38.23 

58 

87.20     33.41 

86.01      34.69 

84.77     35.93 

83.50     37.12 

82.18     38.26 

60 

87.16     33.46 

85.97     34.73 

84.73     35.97 

83.46     37.16 

82.14     38.30 

62 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  6 — Continued 
STADIA  REDUCTION  TABLE 

For  instruments  rated  1  to  100 
In  the  column  "  Hor.  Dist."  find:    100  cos2  a 
In  the  column  "  Diff.  Elev."  find:    100  sin  a  cos  a 
Rod  Vertical 


Mm. 

25° 

26° 

27° 

28° 

29° 

Hor.        Diff. 

Hor.        Diff. 

Hor.        Diff. 

Hor.        Diff. 

Hor.        Diff. 

Dist.       Elev. 

Dist.       Elev. 

Dist.       Elev. 

Dist.       Elev. 

Dist.       Elev. 

0 

82.14     38.30 

80.78     39.40 

79.39     40.45 

77.96     41.45 

76.50     42.40 

2 

82.09     38.34 

80.74     39.44 

79  .34     40  .  49 

77.91     41.48 

76.45     42.43 

4 

82.05     38.38 

80.69     39.47 

79.30     40.52 

77.86     41.52 

76.40     42.46 

6 

82.01     38.41 

80.65     39.51 

79.25     40.55 

77.81     41.55 

76.35     42.49 

8 

81.96     38.45 

80.60     39.54 

79.20     40.59 

77.77     41.58 

76.30     42.53 

10 

81.92     38.49 

80.55     39.58 

79.15     40.62 

77.72     41.61 

76.25     42.56 

12 

81.87     38.53 

80.51     39.61 

79.11     40.66 

77.67     41.65 

76.20     42.59 

14 

81.83     38.56 

80  46     39.65 

79.06     40.69 

77.62     41.68 

76.15     42.62 

16 

81.78     38.60 

80.41     39.69 

79.01     40.72 

77.57     41.71 

76.10     42.65 

18 

81.74     38.64 

80.37     39.72 

78.96     40.76 

77.52     41.74 

76.05     42.68 

20 

81.69     38.67 

80.32     39.70 

78.92     40.79 

77.48     41.77 

76.00     42.71 

22 

81.65     38.71 

80.28     39.78 

78.87     40.82 

77.42     41.81 

75.95     42.74 

24 

81.60     38.75 

80.23     39.83 

78.82     40.86 

77.38     41.84 

75.90     42.77 

26 

81.56     38.78 

80.18     39.  8C 

78.77     40.89 

77.33     41.87 

75.85     42.80 

28 

81.51     38.82 

80.14     39.90 

78.73     40.92 

77.28     41.90 

75.80    42.83 

30 

81.47     38.  8G 

80.09     39.93 

78.68     40.96 

77.23     41.93 

75.75     42.86 

32 

81.42     38.89 

80.04     39.97 

78.63     40.99 

77.18     41.97 

75.70     42.89 

34 

81.38     38.93 

80.00     40.00 

78.58     41.02 

77.13     42.00 

75.65     42.92 

36 

81.33     38.97 

79.95     40.04 

78.54     41.06 

77  .09     42  .  03 

75.  CO     42.95 

38 

81.28     39.00 

79.90     49.07 

78.49     41.09 

77  .04     42  .  06 

75  55     42.98 

40 

81.24     39.04 

79.86     40.11 

78.44     41.12 

76.99     42.09 

75.50     43.01 

42 

81.19     39.08 

79.81     40.14 

78.39     41.16 

76.94     42.12 

75.45     43.04 

44 

81.15     39.11 

79.76     40.18 

78.34     41.19 

76.89     42.15 

75.40     43.07 

46 

81.10     39.15 

79.72     40.21 

78.30     41.22 

76.84     42.19 

75  .  35     43  .  10 

48 

81.06     39.18 

79.67     40.24 

78.25     41.26 

76.79     42.22 

75.30     43.13 

50 

81.01     39.22 

79.62     40.28 

78.20     41.29 

76.74     42.25 

75.25     43.16 

52 

80.97     39.26 

79.58     40.31 

78.15     41.32 

76.69     42.28 

75.20     43.18 

54 

80.92     39.29 

79.53     40.35 

78.10     41.35 

76.64     42.31 

75.15     43.21 

56 

80.87     39.33 

79.48     40.40 

78.06     41.39 

76.59     42.34 

75.10     43.24 

58 

80.83     39.36 

79.44     40.42 

78.01     41.42 

76.55     42.37 

75.05     43.27 

60 

80.78     39.40 

79.39     40.45 

77.96     41.45 

76.50     42.40 

75.00     43.30 

TOPOGRAPHIC  STADIA  SURVEYING  63 

ANDERSON'S  STADIA  REDUCTION  TABLE 

(As  prepared  and  in  use  by  U.  S.  Geological  Survey) 

Explanation  of  Table:  Table  7  is  particularly  useful 
when  topographic  surveys  of  large  areas  are  to  be  made. 
It  was  prepared  by  Mr.  C.  G.  Anderson  and  has  been 
published  by  the  U.  S.  Geological  Survey  in  a  pamphlet 
entitled  "  Tables  for  Obtaining  Differences  of  Elevation," 
1909.  It  is  reprinted  here  with  the  permission  of  the 
Survey.  In  the  U.  S.  G.  S.  pamphlet  the  table  from  0°  to 
5°  angle  of  elevation  includes  rod-readings  to  3500  ft.  though 
here  reproduced  to  only  2600  ft. 

The  figures  in  'the  body  of  the  table  give  "  Differences  in 
Elevation  "  in  feet  for  rod-readings  in  feet,  read  on  a  rod  held 
vertically. 

The  degrees  of  vertical  angle  are  printed  at  the  top  of  each 
page;  the  minutes  in  the  right  or  left-hand  vertical  columns. 

The  figures  in  the  top  horizontal  line  are  the  rod-readings 
(  =  intercept  times  rating  factor). 

The  figures  in  the  bottom  horizontal  line  are  the  correct  hori- 
zontal distances  based  on  the  middle  (30')  angle  of  the  page. 

The  horizontal  distances  were  computed  by  the  formula 


(32) 


To  increase  the  usefulness  of  these  tables,  there  has  been 
added,  at  the  bottom  of  each  page,  a  correction  for  distance 
which  has  been  given  for  each  departure  of  10'  from  the  angle 
for  which  distance  is  noted  in  the  table.  The  basic,  angle 
for  distance,  as  already  stated,  is  in  each  case  the  half  degree. 
For  all  vertical  angles  on  any  page  or  in  any  column  less  than 
this  basic  angle,  i.e.,  above  the  30'  line,  the  correction  will 
be  positive,  it  will  be  added  to  the  distance  at  the  bottom  of 
the  page  or  column  ;  and  for  all  vertical  angles  larger  than  the 
basic  angle,  i.e.,  below  the  30'  line,  the  correction  is  to  be  sub- 
tracted. 


64  TOPOGRAPHIC   STADIA  SURVEYING 

The  differences  in  elevation  were  computed  by  the  for- 
mula: 

h  =r  sin  a  cos  « (33) 

As  elsewhere  explained  in  this  manual  a  somewhat  closer 
approximation,  when  surveys  are  made  with  ordinary  instru- 
ments, can  be  obtained  by  entering  the  table  with  (r+e)  or 
(r+1)  instead  of  with  r.  This  applies  both  in  the  matter 
of  difference  in  elevation  and  distance. 

This  table  as  is  seen  from  the  above  formulas  was  pre- 
pared for  use  as  an  approximation  table  and  in  this  respect 
ranks  with  Table  6.  When  more  than  ordinary  accuracy  is 
required  the  corrections  e  cos  a  and  e  sin  a.  can  be  added  to  the 
values  taken  from  the  table  when  entered  with  the  rod- 
reading  r. 

Tabular  values  for  the  omitted  columns,  viz. :  1000,  2000, 
and  3000,  can  be  obtained  from  columns  100,  200  and  300, 
respectively,  by  moving  the  decimal  point  one  place  to  the 
right. 

Tabular  values  beyond  the  range  of  the  table  can  be  ob- 
tained by  moving  the  decimal  point  to  right  or  left,  as  shown 
in  the  following  example: 

Required  the  difference  in  elevation  for  an  angle  of  3°  16' 
for  a  rod-reading  of  3644  ft.  (i.e.,  intercept  of  half  stadia 
interval,  18.22  times  200=3644  ft.).  In  this  case  (r  +  1) 
=  3645  ft. 

For  3000  ft.  (from  300  ft.  moving  the  deci- 
mal to  right) 170.7  ft. 

For  600  ft 34.1  ft. 

For  40  ft.  (from  400  ft.  moving  the  deci- 
mal point  to  left) 2.28  ft. 

For  5  ft.  (from  500  ft.  moving  the  deci- 
mal point  two  places  to  left) .28ft. 


Difference  in  elevation. .  207.4  ft. 


TOPOGRAPHIC  STADIA  SURVEYING  65 

The  distance  in  the  case  of  this  example  is  found  by  the 
aid  of  the  table  to  be  3634  ft.,  as  follows: 

For  3°  30' 

For  3000  ft.  (from  300  ft.  moving  the  deci- 
mal point  to  right) 2989  ft. 

For  600  ft 598ft. 

For  40  ft.  (from  400  ft.  moving  the  decimal 

point  to  left) 40  ft. 

For  5  ft.  (from  500  ft.  moving  the  deci- 
mal point  two  places  to  left) 5  ft. 

Distance  from  table 3632  ft. 

For  3°  16'  being  14'  less  than  3°  30'  add: 

1,4  X36.3  X .035  =  1.78  or 2  ft. 

Corrected  distance  is .  .  3634  ft. 


66 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 

DIFFERENCES   IN    ELEVATION 
0° 


' 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

; 

03 

03 

03 

0.8 

3 

5 

o  09 
o  15 

o  29 

0  44 

o  6 

0  7 

09 

1    0 

?! 

I    0 

'   3 

i   3 
i  6 

1   4 
I   7 

'5 
'  9 

23 

8 
9 

o  23 

0    26 

0  46 

n^ 

o.  70 
o  79 
o  87 

09 

I    0 

I    2 

i  3 

'•  4 
I   6 

i  6 
i   8 

'   9 

2    1 

i  6 
2  9 

7    8 

3  ' 

2    6 

.3  o 
34 

II 
•3 

o  32 
o  35 
o  38 

o  64 
o  70 
o  77 

96 
•  3 

'3 

I    4 
'5 

i  6 
i   7 
'  9 

1-9 

2  3 

2    3 
2    4 

2    6 

7    6 

i  8 
3  o 

2   9 
3   ' 
3  4 

1:1 

4   2 

.38 
4   2 
4  5 

4    2 
45 
4-9 

'5 

0  44 

o  87 

3' 

1   7 

2    2 

2    6 

3   I 

35 

3  9 

4  8 

52 

5-  7 

I? 
18 
'9 

0  49 
0.52 
o  55 

o  99 
'05 

.48 
•57 
66 

2    I 

2    5 
2   6 

3  > 

3  5 
3-7 

4-  0 

4   2 

4  4 
47 

5  4 
58 

5  9 
6  3 
66 

64 
6.8 

7    2 

20 

21 
22 
'3 

0.58 

o.  61 
0.64 
0.67 

I.  16 

I.  22 
1.28 

>  34 

•75 

•83 
•92 
.  01 

24 
2.6 

3  > 

32 

1:1 

4  3 
4-5 

47 

49 
5   ' 

5  5 
5-8 

.    6.7 
7  o 

7  3 
7  7 

79 
83 

»5 

o  73 

J-45 

.  18 

8  7 

94 

27 

0-79 

'•57 

•36 

3-  ' 

39 

4-  7 

5  5 

6  3 

7   i 

8  6 

94 

10   2 

29 

o.84 

i.69 

•53 

3-4 

4-2 

5  ' 

5  9 

6  7 

7  6 

9  3 

10    1 

II     I 

3' 
32 

o.  90 
o-93 

i.  so 

1.86 

7° 
79 

3-6 

3-7 

4  5 
4-7 

54 
56 

63 
6  5 

7    2 

7  4 

8   i 

8   4 

9  9 

10    2 

I  1    2 

II    7 

12     1 

34 
35 

36 

s 

39 
40 

4> 
42 
43 

o  99 

1    02 

05 

.08 

:ii 

•'9 

.  22 

:li 

1.98 
2.04 

2.09 
2-15 

2.  21 
2.27 

2-33 

2.38 

2.44 
2.50 

97 
3  °5 

3-  '4 
3-23 
3-32 
3-40 
3-49 

3-58 

3-66 
3-75 

4.0 
4.1 

42 
4-3 
4-4 
4-5 
4-7 

4-8 
4-9 
5-o 

49 

5   l 

52 
54 
5-5 
5-7 
5-8 

6.0 
6.1 

6.2 

5  9 
6  i 

63 
65 
66 
6  8 

72 

7-3 
7-5 

6  9 
7   > 

7  3 
75 
77 
8.0 
8  i 

1:1 

8.8 

7  9 
8   i 

8  4 
8  6 
8  8 
9  ' 
93 

9-5 
9.8 

10.  0 

8  9 

9    2 

9  4 
97 
9  9 

10    2 

10.5 
10.7 

II    0 
II     2 

10  9 

"   5 
n   8 

'2  5 

12    8 

'3   ' 
'3-4 
13  8 

ii   9 

12    2 

12   6 
12    9 

'3  3 
'3  6 
14  o 

'43 
'4-7 
15  o 

12    9 

'3  -2 

'3  6 
14.0 
14.4 
'4-7 
'5   ' 

15-5 
'5-9 
16  2 
16  6 

45 
46 

•31 

•34 

2.62 

2.63 

3  93 

01 

•5-2 

5-4 

6-5 
6.7 

7.8 
8.0 

9.2 
94 

10.5 
10  7 

ii  8 

12    0 

14.4 
14-7 

'5-7 
16  i 

17  o 
'74 

48 
49 
50 

5» 
52 

53 
54 
55 

56 
57 
58 
$9 

.40 
•42 
•45 

.48 
•51 
•54 
•57 
.60 

.:8 
.69 

•7.2 

2.79 

2.85 

2.91 
2.97 

3-02 

3-o8 
3-14 
3-20 

3-«6 
3-32 
3-37 
3-43 

'9 
28 
36 

45 
54 
4.62 
4-7' 
4.80 

4.88 
4-97 
5-o6 
5-  '5 

56 
5-7 
5-8 

11 

6.2 

6-3 
6.4 

6-5 
6.6 
6-7 
6.9 

7-0 
7-  ' 
7-3 

7-4 
7-6 
7-7 
78 
8.0 

8.1 
8-3 
8-4 
8.6 

8.4 
8.6 
8-7 

8.9 
9-  i 

9-2 

9-4 
9.6 

9.8 
9-9 

10.   I 

10.3 

9-8 
10  0 
10.  2 

10.4 

10.8 

0 
2 

4 
6 
.8 
0 

"  ii.  a 

II.  4 
ii.  6 

II.  9 
«  3 

12    6 
12.8 

'3-3 
'35 
•37 

12.6 
12    8 

13  ' 

"34 
36 
3-9 
4  i 
4-4 

4-7 
49 
5-2 

5  4 

•54 
'5-7 
16.0 

163 
16.6 
17.0 
'73 
17  6 

'79 
18  2 
18.6 
18  9 

16.8 
17   ' 
'74 

17.8 
18  2 

;«8.i 
19.2 

'95 

19.9 

20.  2 

>o  6 

18.  i 
.8.5 
18  9 

'93 
'97 
20.0 

20.4 

20.8 

21.  2 
21    & 

21    9 

22.3 

Horz. 
Dist. 

99-99 

»99-9 

299-9 

399-9 

499-9 

599-9 

699.9 

7999 

899.9 

1099.9 

1199.9 

12999 

Hor.  dist.  Is  for  30'  point.     Add  or  subtract  .005  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


67 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 
0° 


1400 

1500 

1600 

1700 

1800 

1900 

2100 

2200 

2300 

2400 

2500 

2600 

f 

I.O 

,., 

i  8 

0.6 

0.7 

o.  7 

0.7 

0.8 
"5 

2 

1.6 

24 

2.8 

2.6 

3-o 

28 
33 

3-o 
3-5 

3-  ' 
3-7 

3-3 
3-9 

3-7 
4-3 

3-8 
4-5 

4.0 
47 

3-5 
4-  2 
I'l 

3-6 
4-4 

H 

3-8 

4-S 
5-3 

5 

6 

7 
g 

3-7 

3-9 

4-  2 

4-  4 

4-7 

5-o 

l\ 

it 

6.0 
6  7 

6-3 

6.6 

6.8 
7  6 

9 

4-5 
49 
5-3 

4.8 

5-2 

5-7 

5-  ' 
56 
6.0 

5-4 
59 
6.4 

5-8 
63 
68 

6.  i 
6.6 

7   2 

6.7 
73 
79 

7-  o 
7-7 
8.3 

7-4 
8.0 
8.7 

77 
8.4 
9  ' 

8.0 
8.7 
9-4 

8-3 

K 

ii 

12 

«3 

6.  I 
6-5 

65 

7.0 

7-4 

79 

8.  2 

9  2 

9-8 

9.6 

10.  2 

10.  7 

10.5 

II.  2 

10.9 
it.  6 

11.3 

12.  I 

'5 
16 

6.9 
73 
77 
8.  i 

86 
9.0 

7-4 
78 
8-3 
8.7 

H 

79 
8.4 
8.8 
9-3 

9.8 

10.  2 

8.9 
9-4 

10.  0 

10.4 
10.9 

9-4 
9-9 
16.5 

II    0 

•  9-9 
10.  j 
II.  i 

II  6 

II.  0 

ii  6 

12.  2 
12.8 

"5 

12.  2 
12    8 

3-4 
4-  7 

12.7 
<3-4 

14  0 
'47 
«5-  4 

:;:8 

•33 

14.0 

'4-7 

|l:t 

12-4 

ii 

'5-3 
16.0 
16.7 

12.9 
13-6 
14.4 
I5-I 

'5-9 

16.  6 
•  7-4 

17 
18 
'9 

20 

21 
22 
23 

9-8 
IO.  2 

10.6 

II  0 
II  4 

10.9 
;:i 

12    2 

II  6 

13.  I 
13  6 

'30 

12.4 

12  9 
'33 
•3-8 

>3  ' 

•  3-6 
'4   I 
'4  7 

13-8 

14.4 
14-9 
'5  5 

>5-3 

«5-9 
i6.6 
17  ' 

6.0 

6.6 
7  3 
7  9 

16.7 

17  4 
18.  i 
18.7 

«7  4 

«8.  2 

18.  8 
'9-5 

18.2 

18.9 
19.6 
20.4 

18.9 

19-7 
20.4 

21.  2 

24 
25 

26 
27 
28 

12  6 

'3  ' 

13  5 

14  o 
14.  4 

14.8 
IS  3 

'57 
16.  2 

16  6 

17  i 

18  3 
18.9 

9.2 
19.8 

20.  I 

20.9 

21    8 

22    7 

3° 

13.0 

'3  4 

14.  0 
14.4 

'49 

'54 

'5-8 
,6.3 

16  8 
'7  3 

18.  2 

20.  2 

21    I 

22    I 

23.0 

24.0 

25.0 

33 

14  2 
14.7 

'5  ' 
•5  5 

15-3 

'57 
16   I 
16  6 

16.3 

16.7 
17.2 
17-7 

'7  3 

17  8 
'8.3 

18  8 

18.3 

18  8 
19.  4 

'93 

19.  9 
20  4 

21    4 

22   0 
22   6 

22    4 

23.0 
23-7 

23-4 

24.  I 
24  7 

24.4 

III 

26.5 

25-4 

26.2 
26.9 
27.6 

26.5 

27    2 
28.0 
28.7 

35 

36 
37 
38 

15  9 

16.3 

16.7 

17  o 
17  4 

17  9 
18  3 

18.  2 
18.6 

19.  I 

»9-3 
19.8 

20.3 

20.  4 

20.9 

2'    5 

22    I 

22   7 

24.4 
25-0 

25  6 

26.2 
26  9 

26.  I 
26.8 

27-4 
28   I 

27.2 
27.9 

28.6 

28.4 
29.1 

29.8 

29-5 
30.2 

3'  o 

31.  8 

39 
40 

4> 

42 

17  5 
17  9 
18.3 

18.7 
19  ' 
19  5 

18.  8 
19.2 
19.6 

20.  I 
20.5 
20  9 

20.0 

20  5 
20.  9 

21.4 

21  9 

22.3 

21:2 

21.8 
22.  2 

22.7 
23.2 
23-7 

2?.  5 
23.  o 

23.6 

24.  « 

24.6 

25  ' 

3-8 
4-3 
4-9 

« 

26.5 

26.3 
26-9 
27-5 

28.1 
28.7 
29-3 

27-5 
28.2 
28.8 

29-4 
30.1 
30.7 

28.8 
29.4 
30.  I 

30.8 
3'-4 
32-  I 
32.  8 

30.0 
30.7 
3'-4 

32  ' 
32.8 
33-5 

3'.  3 
32.0 
32-7 

33-4 
34-2 
34-9 
35-  6 

32-5 
33-3 
34-o 

34-8 
35-5 
36.3 
37-0 

43 
44 

45 

46 
47 
48 
49 

20.4 
20.8 

21    8 

22    2 

23-3 
23-7 

*4-7 
25.2 

26.2 

26.7 

27.6 

28.2 
28.7 

3°-5 
31-2 

3'-8 

32.0 

32.6 
33-3 

33-4 

Sti 

34-9 

35-6 
36.3 

36-4 

37-  « 
37-8 

37-8 

38.6 
39-3 

50 

5» 

5* 

21.6 
22  4 
22.8 

£6 
24.0 

36 

4.0 

4-4 
4-9 
5-3 
5-7 

25.  t 
25.6 

26.1 

26.5 

27  5 

26.7 
27-2 

27-7 
28.2 
28.7 
29.2 

28.3 
28.8 

29.3 
29.8 
30.4 

3°  9 

29.8 
30-4 

30.9 
3'-5 
32.0 
32.6 

33-o 
33-6 

34-2 
34-8 
35-4 
36.0 

34-5 
35-2 

35-8 
36  5 
37-  ' 
37-8 

s; 

s? 

38.8 

39  5 

37-7 
38-4 

39-  ' 
39-8 
40.5 
41.2 

38.5 
39-2 

40.7 
4'-4 
42-2 
42-9 

40.1 
40.8 
41.6 

42-3 
43-' 
43  9 
44-6 

53 

54 
55 

56 

5 

59 

13999 

14998 

15998 

16998 

i799-» 

1899.8 

2099-8 

2199* 

2299.8 

2399^ 

2499.8 

2599-8 

Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .005  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


68 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 
1° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

o 

2 

3 

4 
5 

6 

I 
9 

10 

11 

12 
13 

u 

'5 
16 

•74 
77 
.80 
-83 
86 
•89 

•  9* 
95 
98 

01 

04 

06 
09 

12 

IS 

21 

3-49 
3  55 
3-6r 
3-66 
3-72 
3-78 

3-84 
3  90 
3  96 
4.01 
4.07 

4->3 
4-  19 
4-^5 
4-30 
4.36 

4-42 

5-24 
5-32 
3-4' 
5-50 
5-58 
5-67 

je 

5-93 
6.  02 
6.  ii 

6.19 
6.28 
6.37 
6.46 
6.54 

6.63 

7.0 
7-» 

8-7 
8.9 

10.5 
10.6 

12.2 

12.4 

14.0 
14.2 

15-7 
16.0 

19  2 

'9'n 

20.9 
21   3 

22.7 
23  i 

7-3 
7-4 
7-6 

7-7 
7-8 

80 
8.1 

8.3 
8-4 
8-5 
8.6 

8.7 

8.8 

9.2 
9-3 

11.  O 
11.  2 

12.8 

13-0 

'4-7 
14.9 

'65 

16.7 

20.  1 

2°1 

22.  O 
22-3 

23  8 
J4-2 
24  6 

24.9 

9-6 
9-7 
9-9 

ro.  2 

10.3 
10.5 
10.6 
10.8 

10.  t 
II.  O 

11.  S 

«3-4 

>5-4 

'73 

21.  I 

2    .0 

11.9 

12.0 
12.  2 

12.4 
12.6 
12.7 
12.9 
13-  > 

'3-3 

'38 
14.0 
14.2 

«4  4 
«4-7 
14  -9 
15-' 
'.5-3 

«S-5 
>5-7 
'5-9 
J6.  i 
•  6.3 

16.5 
16.7 
16.9 
'7-«. 

'5-8 
'63 

•6.5 
16.7 
17.0 
17.2 
»7-4 

«7  7 
17.9 
18.  i 
18.4 
18.  6 

18.  8 
19.  i 
«9  3 
'95 

17.8 
18.  i 
18-3 

18.6 
18.8 
19.1 
19.4 
19.6 

19.9 

20.  2 
2O.  4 
20.7 
20.9 

21.2 
21.5 
21    7 

22.  0 

21.7 
22.4 
22   7 

23  o 

23  3 
23-7 
24.0 

24  3 
24  6 
24  9 
25-3 
256 

25-9 

26    2 

26  5 
26  9 

2      7 
2    -4 

248 

25  ' 

III 

26.2 
26.5 

26  9 
27.2 
27.6 
27  9 

28.3 
28.6 
29.0 
29  3 

25-7 
26.  i 
26.5 

26.8 
37.1 
27-6 
28.0 
28.4 

28  7 
29  ' 
29  5 
29.9 
30.2 

30-6 
31.0 
3'   4 
31.8 
32   i 

32  5 
32  9 
33  3 

18 
«9 
20 

21 
22 
23 

24 

'5 
26 

r. 

•       »9 
30 

3i 
32 
33 
34- 
35 

36 

i 

39 
40 

4< 
4' 
43 
44 
45 

46 
47 
48 
49 
5° 

5' 

52 
53 
54 
55 

56 

8 

59 

27 

3° 
33 

5 

41 

44 
47 

5° 

51 
59 
62 

65 
68 
70 
73 
76 

79 
82 

It 
9- 

94 
97 

00 

.02 
3  05 

308 
3  «> 
3  M 
3  "7 
3  20 

3  23 
3.26 
3-29 
3-3' 
3  34 

3  37 
3  40 
3  43 
3  46 

4  54 
4-59 
4  65 

4-7" 

4-  77 
4-83 
4.88 
•4-94 

5  oo 
5  06 
5  12 
5  '8 
5  23 

5  29 
5  35 
54' 
5  47 
5  52 

5  58 
5  64 
5  70 
5  76 
5.8i 

5  8'/ 
5  93 
5  99 
6  05 

6.80 
6.89 
6.98 

7.07 
7  IS 
7-24 
7  33 
74' 

7  50 
7  59 
7.68 
7-76 
7  85 

794 

8  02 

8  n 
8  29 

8  37 
846 
8-55 

9  ' 
9.2 
93 

9-4 
95 
9.6 
9.8 
9-9 

0.0 
0.  1 
0   2 
0  4 

°-  5 

07 
0.8 

o.  9 

1    0 

I  3 

"  3 
"•5 
11.  6 

11.8 
11.9 

12.  1 
12.  2 
12.  4 

12    5 
12.6 
12    8 
12.9 

13-6 
'3-8 
14.0 

14.  i 
»4-3 
'4-5 
•47 
14-8 

15-0 
"S* 
'54 

'55 

'75 
'7-7 
'7  9 

20.0 

20  5 

III 

23.0 

27i 

28  1 

30  o 
30.3 
30-7 

'3  2 
•34 
'3  5 

!« 

>4  0 
14   1 

'5  9 
>6.  o 

16    2 

16  4 
16.  6 

16  7 
16  9 

\il 

18.9 
19  1 
'9  3 

'95 
19.7 

21    2 
21    4 
21    6 
21    9 
22    1 

22    3 
22    6 

38 
4   ' 
43 
46 
24  9 

25  ' 

J5-  4 

29.  1 

29  4 
29.  7 
30  1 
30  4 

30  7 
3'  o 

3'   4 

3     8 
32   ' 

il.3 

33"' 

33  5 
338 

34  0 

34  4 
34  8 
35  2 
35  5 
35  9 

36  3 
36  7 

872 

8  81 
8  90 
8.98 
9.07 

i  6 

'4  5 

'7  4 

20  3 

23    3 

26    2 

26.4 
26.7 

27.  o 

3"   7 

32  3 
32  6 
32  9 
33  3 
33  6 

33  9 

34-2 
34  5 
34-8 
35  2 

35  5 
35  8 
36-1 
36.4 
36-8 

37  « 

37-4 
37-7 
380 

34  5 
34  9 

35  * 
35  6 
35  9 
36  3 
36  6 

37  o 
37-3 
37  7 
38.0 
38-4 

387 
39-' 
39  4 
39-8 
40.1 

40  5 
40.8 

41    2 

4'   5 

37  4 
37  8 

3&  •' 
386 
38  9 
39  3 
39  7 

40.  i 
40.4 
40  8 
4'   2 
41   6 

41   9 
42-3 
42  7 
43  ' 
43  4 

43  8 
44  .2 
44  6 
45  0 

'  9 

2    1 

zi 

>5  o 
15  ' 

17.8 
18.0 

20.8 
21.0 

23-7 

24  o 

6.  16 
6   22 
6.28 
6-34 
6.40 

[?, 

6-57 
6.63 
6  68 

6.74 
6.80 
6.86 
6.92 

9.24 
9-33 
9.42 
9  50 
9  59 

9.68 
9  77 
9  85 
9  94 

10.  20 
10.29 
.0.38 

2    3 
24 
2  6 
2-7 
12.8 

12.9 

13  ' 

'32 

«3  4 

13  5 

'36 
"3-7 
•38 

Si 

«5  7 
'58 
16.  o 

16.  1 
>6.3 
16  4 
16  6 
16.7 

16.9 
17.0 
17.2 
«7  3 

•8-5 
18.7 
18  8 
19.0 
19.2 

'94 
'95 
19.7 
19.9 

20.  I 
2O.  2 
20.6 

20.7 

21    6 
21.8 

22.  2 

22.4 

22.6 
22    8 
23.0 
23-2 
23-4 

23-6 
23-8 
24.0 
24.2 

246 
24.9 
25    ' 
25-3 

25  6 

25  8 
26.0 
26.3 
26.5 
26.7 

27.0 

27   2 
27  4 
27  7 

27  5 

27.7 
28.0 
28.3 
28.5 
28.8 

29.0 
29  3 
29.6 
29.8 
30.1 

303 
30  6 
30  9 

3'    ' 

Horz. 

i".!. 

99-93 

199.9 

2998 

399-7 

499-6 

599 

699 

799 

899 

1099 

"99 

1299 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .015  ft.  to  each  100  ft. 
distance  for  each  10'  departure. 

TOPOGRAPHIC  STADIA  SURVEYING 


69 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 
1° 


1400 

1500 

1600 

1700 

1800 

1900 

2100 

2200 

2300 

2400 

2500 

2600 

f 

24.  4 

26.2 

27.9 

29-7 

3>  4 

33-2 

36.6 

38.4 

40.  i 

41.9 

43  6 

45-4 

0 

24  8 

26.6 

28.4 

30.2 

3'  9 

33-7 

37-2 

39  o 

40.8 

42.6 

44-  4 

46.1 

i 

25  2 

27.0 

28.8 

30.6 

32.4 

34-3 

37-9 

39  7 

4'  5 

43-3 

45  ' 

46.9 

2 

25  6 

27-5 

29-3 

3'  ' 

33-o 

34-8 

38.5 

4°-3 

42.  i 

44-o 

45  8 

47.6 

3 

26.  i 

27.9 

29.8 

3'  6 

33-5 

35-4 

39-  i 

40.9 

42.8 

44-7 

46.5 

48.4 

4 

26.5 

28.4 

30.2 

32-  ' 

34  o 

35-9 

39-7 

4..  6 

43-5 

45-4 

47-3 

49  ' 

5 

20.  8 

28.8 

3°  7 

32.6 

34-  S 

36.5 

40.3 

42.2 

44-  ' 

46.  i 

48.0 

49-9 

6 

27  3 

29.2 

3'  2 

33  ' 

35-  « 

37  o 

40.9 

42.9 

44  8 

46.7 

48.7 

50.6 

7 

27  7 

29.7 

3'-  6 

33-6 

35-6 

37-6 

4'-  5 

43  5 

45  5 

47-5 

49-  4 

5'-4 

8 

28.  I 

30.  i 

32-  I 

34-  ' 

36.1 

38.« 

44-  ' 

46.1 

48.2 

50.  2 

52.2 

9 

28.5 

30.5 

32-6 

34-6 

36.6 

38.7 

42  7 

44-  8 

46.8 

48.8 

50.9 

52.9 

10 

289 

3'  o 

33  o 

35-  » 

37  2 

39  * 

43  3 

45-4 

47-5 

49  5 

5'  6 

53-7 

,, 

29-3 

3>-4 

33-5 

35  6 

37-7 

398 

44.0 

46.1 

48.2 

50  3 

52.4 

54-4 

12 

29-7 

31-8 

34-0 

36.1 

38-2 

4°  3 

44  6 

46.7 

48.8 

5°-9 

53  ' 

55-2 

'3 

3°  ' 

3*-3 

34  4 

36.6 

38.7 

40.9. 

45-2 

47  3 

49  5 

5>  6 

53  8 

55  9 

14 

30-5 

3*  7 

34  9 

37  i 

39  3 

41  4 

458 

48  0 

50.2 

52  3 

54  5 

56.7 

'5 

3°  9 

33  2 

35  4 

37-6 

398 

42  o 

46.4 

48.6 

50.8 

53  o 

55  2 

57-5 

16 

31-  3 

33  6 

35-8 

38.1 

40.3 

42  5 

47  0 

49-3 

5'  5 

53  7 

56  o 

58.2 

'7 

3»  7 

36.3 

38.6 

40.8 

43  ' 

47  6 

49  9 

52  2 

54-4. 

56.7 

59  o 

18 

32  2 

34  5 

36.8 

39  o 

4'  3 

43  6 

48.2 

50.5 

52.8 

55.' 

57  4 

59  7 

'9 

32  .6 

34  9 

37-2 

39-6 

41.9 

44  2 

48.9 

5'  2 

53  5 

55  8 

58  3 

60  5 

20 

33  ° 

35  3 

37  7 

40.0 

42.  4 

44.8 

49  5 

5-8 

54  2 

56  5 

58  9 

61.  2 

2I 

33  4 

35  8 

£j 

40.5 

42.9 

45  3 

5°  I 

5*  5 

54  8 

57  2 

59  6 
60  i 

62  0 

62  8 

22 

33  8 

34  2 

36  2 

36  6 

39  ' 

4'  5 

44.0 

46.4 

5°  7 
5'  3 

53  ' 

53  7 

55-  5 

56.2 

57  9 
58  6 

oo  3 
61  i 

63  5 

23 
24 

34  6 

37  i 

39  5 

44  5 

47  o 

5'  9 

54  4 

56  8 

59-3 

6.  8 

64  3 

25 

35  ° 

37  5 

40.  o 

42  5 

45  o 

47  5 

52  5 

55  -o 

57  5 

60.0 

62  5 

65  o 

26 

35  4 

37  9 

40  5 

43  0 

45  5 

53  ' 

55  6 

58.2 

60  7 

63  2 

65  8 

27 

35  8 

38  4 

40.9 

43  5 

46  0 

48  6 

53  7 

56.3 

58.8 

61  4 

64  0 

66  5 

28 

36  2 

388 

41  4 

46.6 

49  2 

54-3 

56  9 

59  5 

62  i 

64  7 

67  3 

29 

366 

39  3 

41  9 

44  5 

47  i 

49  7 

55  o 

57  6 

60  2 

62  8 

65  4 

68  o 

3° 

J?  o 

39  7 

42  3 

45  0 

47  6 

5°  3 

55  6 

58  2 

60  9 

63  5 

66  2 

68  8 

3' 

37  4 

42  8 

45  5 

48  2 

50  8 

56.2 

58  8 

61  5 

64  2 

66.9 

69.6 

32 

37  9 

40  b 

43  3 

48  7 

5"  4 

56  8 

59  5 

62  2 

64.9 

67  6 

70  3 

33 

3»  3 

41  o 

43  7 

46  5 

49  2 

5'  9 

57  4 
58  o 

60.  I 

60.  8 

62  9 

6l  e 

65  6 

66  i 

68.3 

7'  ' 
71  8 

34 

39  > 

41  y 

44  7 

47  4 

50  2 

53  o 

58  6 

61  4 

°3  5 

64  2 

oo.  3 

67  o 

698 

72  6 

35 
36 

39  5 

4?  3 

45  ' 

47  9 

50  8 

53  6 

59  2 

64  9 

67  7 

70  5 

73  3 

37 

39  9 

42  7 

45  6 

48  4 

5'  3 

54  i 

598 

62  7 

65  5 

68.4 

71  2 

74  ' 

38 

40  3 

43  •* 

46  0 

48  9 

5'  8 

54  7 

60.4 

63  3 

66.2 

69.1 

72  0 

74  8 

39 

40  7 

43  & 

46.5 

49  4 

52  3 

55  2 

64.0 

66.9 

69  8 

72  7 

75  6 

40 

4>  • 

44  0 

47  o 

49  9 

52  9 

55  8 

61  7 

64  6 

67  S 

70.5 

73  4 

76  3 

4> 

41  5 

4>  9 

44  9 

47  9 

5°  9 

53  9 

56  3 
56  9 

62  3 
62  9 

65  9 

68.9 

71.9 

74  9 

77  9 

43 

42  3 

45  3 

48  4 

5'  4 

54  4 

57  4 

63  5 

66.5 

69  5 

72  6 

75  6 

78  6 

44 

42  7 

45  8 

488 

5'  9 

54  9 

580 

64  i 

67.2 

70.2 

73  3 

76.3 

79  4 

45 

43  ' 

40  i 

49  3 

S2  4 

55  5 

58  5 

64-7 

67  8 

70  9 

74  o 

77  0 

80.  i 

46 

43  5 

46  7 

49  8 

52  9 

56  o 

59  ' 

65-3 

68  4 

71.5 

74  6 

77  8 

80.9 

47 

43  9 

47  ' 

5°  2 

53  4 

56  5 

59  7 

65.9 

69.1 

72  2 

75  3 

78  5 

81  6 

48 

44  4 

47  5 

50  7 

53  9 

57  o 

60  2 

66.5 

69  7 

72  9 

76  o 

79-2 

82.4 

49 

44  » 

48  0 

51  2 

54  4 

57  6 

60  8 

67  ' 

70.3 

73  5 

76  7 

80.0 

83  ' 

SO 

45  2 

4»  4 

5'  0 

54  » 

58.1 

6i.3 

67  8 

.  0 

74  2 

77  4 

80.7 

83.9 

5' 

45  6 

48.8 

52  i 

55  3 

58.6 

61.8 

68  4 

.  6 

74-9 

78.1 

81  4 

84  6 

52 

46  0 

49  3 

52  6 

55  8 

59  ' 

62.4 

69.  o 

3 

75  5 

78  8 

82.  i 

85  4 

53 

46.4 

49  7 

53  0 

56  3 

59  6 

63  o 

69  6 

9 

76  2 

79  5 

82.8 

86  2 

54 

46.8 

50.1 

S3  5 

56.8 

60.  2 

63  5 

70  2 

3  5 

76  9 

80.2 

836 

86.9 

55 

4?  2 
47  6 

50  6 

53  9 

57  3 

60.7 

64  i 

70  8 

74  * 

77  6 

80  9 

84  J 

Q-   .. 

»7  7 

88  4 

56 

48  o 

5'  5 

54  4 
54  9 

57  " 
58  3 

61  7 

65  2 

72  o 

75  5 

78  9 

82  j 

Ill 

89  1 

5$8 

48  4 

5'  9 

55  3 

58-8 

62  3 

65  ? 

72  6 

76  i 

79  6 

83  o 

86  5 

89  9 

59 

'399 

'499 

'599 

1699 

'799 

1»99 

2098 

2,98 

2298 

2398 

2498 

25?8 

Horz 
Dist. 

Hor.  dist.  is  for  30'  ppint.     Add  or   subtract  .015  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


70 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
3° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

0 

3  49 

6  98 

10  46 

14  O 

I?  4 

20.9 

24.4 

27  9 

31  4 

38.4 

41  9 

45-3 

1 

3  52 

7  03 

10  55 

14  1 

17  6 

21  1 

24.6 

28.  i 

31  7 

38  7 

42  2 

45-7 

2 

3 

3  55 

3  58 

7  09 

10.  64 

"4  2 

17  7 

21  3 

24.8 

28.4 

3'  9 

32.2 

39-0 
39  3 

42.6 

42  9 

46.1 
46.5 

4 
S 

360 
3  63 

7  21 

7  '7 

.0.81 
10.90 

14  5 

18  2 

21  8 

25  4 

29.  I 

32  4 
32  7 

396 
40.0 

43  2 
43  6 

46.8 
47-  » 

6 

3  66 

7  32 

10  99 

14.6 

18  3 

22.  O 

•25  6 

29  3 

33  o 

40  3 

43  9 

47-6 

7 

3  69 

7  38 

u  07 

14.8 

18  5 

22  1 

25,8 

29  5 

33-2 

44  3 

48.0 

8 

3  72 

7  44 

11  16 

14.9 

18  6 

22  3 

26.0 

29.8 

33  5 

40.9 

446 

48.4 

9 

3  75 

75° 

u  25 

15.0 

18.7 

22  5 

26.  2 

30.0 

33  7 

41  2 

45  -o 

48.7 

3  78 

7  5« 

ii  33 

15  I 

18  9 

22-7 

26.4 

30.2 

34-° 

41  6 

45-3 

49-1 

it 

3  81 

7  61 

li  42 

•  5  2 

19.  o 

22  8 

26.6 

3°  S 

34  3 

41.9 

45  7 

49-5 

1  3 

384 

7  67 

II  Si 

15  3 

19  2 

23  o 

26  8 

30.7 

34  5 

42  2 

460 

49  9 

13 

3  86 

7  73 

11  60 

IS  5 

19  3 

23  2 

27  i 

30.9 

34  8 

42  5 

46.4 

50.2 

>4 

3  89 

7  79 

11.68 

15  6 

19  5 

23  4 

»7'3 

3  i 

35  -o 

42.8 

46  7 

50.6 

'5 

3  92 

7.85 

ii  77 

15-7 

19.6 

23  5 

27  5 

3  4 

35  3 

43  « 

47  i 

51  0 

16 

3-95 

79° 

II  86 

•58 

19.8 

»3  7 

27  7 

36 

35  6 

43  5 

47  4 

5  4 

I? 

3-98 

7  96 

u  94 

15  9 

19  9 

23  9 

27.9 

3  8 

35-8 
36  i 

43  8 

44.  i 

47  8 
48.1 

5  -7 
5  ' 

>9 

4.04 
4.07 

8.08 
8.14 

12  20 

16.3 

20.3 

24-4 

28.3 
28.5 

3  -3 
3  -5 

36-3 
36.6 

44  4 
44  7 

48  5 
488 

S  -5 
5  9 

21 

4  10 

8.19 

12  29 

16.4 

20. 

24  6 

28  7 

32  8 

36.9 

45  « 

49  2 

S3  3 

22 

4  U 

8  25 

.2.38 

16.5 

20. 

24.8 

28.9 

33-0 

37  i 

45  4 

49  5 

53-6 

»3 

4  16 

8  31 

12  46 

16  6 

20. 

24.9 

29.  i 

33-2 

37-4 

45-7 

49  9 

54-o 

24 

4.  ,8 

837 

12  55 

16  7 

20. 

25  i 

29  3 

33-5 

37  7 

46.  o 

JO.  2 

54  4 

25 

4.21 

8-43 

12  64 

16.8 

21. 

25-3 

29-5 

33  7 

37-9 

46  3 

506 

54-8 

»6 

4  24 

848 

12.73 

17  o 

21 

25  4 

29  7 

33-9 

38.2 

46  7 

50  9 

55  « 

»j 

4  27 

8  54 

12  8l 

17  i 

21. 

25  .6 

29  9 

34  2 

38  4 

47  o 

51-2 

55-5 

26 

4  30 

8  60 

12  90 

72 

21 

25  8 

30.  l 

34-4 

38.7 

47  3 

51  6 

55-9 

30 

4  33 
4  36 

8  716 

13  07 

7  4 

21 

26.  I 

,A   , 

30.  3 
30-5 

34-  6 
34-9 

39-  ° 
39  2 

47  6 
47  9 

48  3 

51  9 

52  3 

52  6 

56-  3 

3* 
33 

4  42 

4  44 

8  831 
8  889 

13  25 

»3  33 

77 
7.8 

22 

20.  3 
26  5 
26.7 

3°-  7 
3°  9 
31-  i 

35-  ' 

35-3 
35-6 

39-  5 
39-7 
40.  o 

48  6 
48  9 

53  o 
53  3 

57.4 
57.8 

34 

4-47 

8947 

13  42 

79 

22 

26  8 

31-3 

35  8 

40.3 

49  2 

53  7 

58  2 

35 

4-50 

9.005 

13-51 

8.0 

22. 

27.0 

3i  5 

36.0 

40-5 

49  5 

54  -0 

585 

36 

4  53 

9.063 

•3  59 

8.1 

22 

27  2 

31  7 

36.2 

40.8 

49  8 

54-4 

58-9 

37 

4-56 

9.  121 

1368 

8.2 

22. 

27  4 

3i  9 

36  5 

41.  o 

50.2 

54-7 

59  3 

38 

4  59 

9-  179 

13-77 

8.4 

22. 

27-5 

32-1 

36.7 

41.3 

50.5 

55-  I 

59-7 

39 

4.62 

9-237 

13-  86 

8.5 

23- 

27-7 

32.3 

36.9 

41  6 

50.8 

55-4 

60.0 

40 

4-65 

9-295 

13-94 

8.6 

23- 

27.9 

32.5 

37  » 

41.8 

51  I 

55-8 

60.4 

41 

4.68 

9  353 

14-03 

8-7 

»3- 

28.1 

32  7 

37-4 

42  > 

51  4 

56.1 

60.8 

42 

4-71 

9.411 

14.  12 

8.8 

23- 

28.2 

32.9 

37  6 

42  3 

56.5 

61.2 

43 

4  73 

9-469 

14.  20 

8-9 

23 

28.4 

33  i 

37  9 

42.6 
42.  9 

52  I 

56-8 
57  2 

61  5 

61  9 

45 

4-79 

9-585 

14.38 

9-2 

24- 

28.8 

33-5 

38^3 

43  I 

52  7 

57-5 

62.3 

46 

4.82 

9.642 

I4  46 

9-3 

j4 

28.9 

33  7 

38.6 

43-4 

53  o 

578 

62.7 

47 

4-85 

9.700 

M  55 

9-4 

24- 

29.  i 

34  o 

38.8 

43  -6 

53-4 

58-2 

63.0 

48 

4.88 

9.758 

14.64 

95 

24- 

29-3 

34-  i 

39  o 

43  9 

53  7 

58.5 

63-4 

49 

4.91 

9.816 

14  72 

9-6 

24- 

29.4 

34-4 

39-3 

44-2 

54-0 

58.9 

63-8 

50 

4-94 

9-874 

14-81 

9-7 

24- 

29.6 

34-6 

39-5 

44-4 

54-3 

59-2 

64.2 

Si 

4-97 

9-932 

14.90 

19.9 

24- 

29.8 

34.8 

39  7 

44  7 

54-6 

596 

64.6 

52 

S-oo 

9.990 

14.98 

20.0 

25- 

30.0 

35-0 

40.0 

45  o 

54-9 

59  9 

64.9 

53 

5-02 

10.  048 

15-07 

20.  I 

25 

,  30.  i 

35-2 

40.2 

45-2 

55-3 

60.3 

65-3 

54 

5-°5 

10.  106 

15-16 

20.2 

25- 

30-3 

35-4 

40.4 

45-5 

55-6 

60.6 

65.7 

55 

5-o8 

10.  164 

15-25 

20.3 

25- 

3°  5 

35-6 

40-7 

45-7 

55-9 

61.0 

66.  i 

56 

5  ii 

10.  222 

IS  33 

20.  4 

25- 

3°  7 

35-8 

40.9 

46.0 

56.2 

61.3 

66.4 

57 

5-14 
5-17 

0.280 

15-42 
15-5' 

20.6 

20.7 

25- 

30.8 
31-0 

36.0 
36.2 

41.  i 
4«  3 

46-3 
46.5 

3ti 

61.7 
62.0 

66.8 
67.2 

59 

5  20 

0.396 

>5  59 

20.8 

26.0 

31-2 

36-4 

41.6 

46.8 

57-2 

62.4 

67.6 

Horz. 
Dist. 

99-8i 

199-6 

299.4 

399-2 

499.0 

599 

699 

798 

898 

1098 

1198 

1297 

Hor.  dlst.  Is  for  30'  point.     Add  or  subtract  .025  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


71 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 
2° 


1400 

1500 

1600 

1700 

1800 

1900 

2100 

2200 

2300 

2400 

2500 

2600 

t 

48.8 

52.3 

55.8 

59-3 

62.8 

66.3 

73-* 

76.7 

80.2 

83-7 

87.2 

90.7 

o 

»9-  2 

56.3 

59-8 

63.3 

66.8 

73-9 

77-4 

80.  9 

84-4 

87-9 

91.4 

i 

<;.  6 

53-  2 

56.7 

60.3 

63.8 

67.4 

74-5 

78.0 

8'i.6 

85-1 

88.6 

92.2 

1 

53-6 

57-2 

60.8 

64-4 

67.9 

75-  ' 

78.6 

82.2 

85.8 

89-4 

93-0 

3 

5°-  5 

54-  i 

57-7 

61.3 

64.  9 

68.8 

75-7 

79-3 

82.9 

86.5 

90.  i 

93-7 

4 

50.9 

54-5 

5S.I 

61.8 

65.4 

69.0 

76.3 

79-9 

83.6 

87.2 

90.8 

94-5 

S 

5  -3 

54-9 

58-6 

62.2 

65.9 

69.6 

76.9 

80.6 

84.'  2 

87-9 

91.6 

95-2 

6 

5  -7 

55-4 

59-  ' 

62.7 

66.4 

70.  l 

77-5 

81.2 

84.9 

88.6 

92-3 

96.0 

7 

5  •« 

55-8 

59-5 

63.2 

67.0 

70.7 

78.1 

81.8 

85.6 

89-3 

93-0 

96.7 

8 

5  •  5 

56.2 

60.0 

63-7 

67.5 

71-2 

78.7 

82.5 

86.2 

90.0 

93-7 

97-5 

9 

5     9 

56.7 

60.4 

64.2 

68.0 

71.8 

79-3 

83.1 

86.9 

90.7 

94-5 

98.2 

10 

53-3 

57  i 

60.  9 

64-7 

68.5 

72-3 

79-9 

83.7 

87.6 

91.4 

95-2 

99.0 

ii 

53-7 

57-5 

61.4 

65.2 

69.0 

72.9 

80.6 

84.4 

88.2 

92.0 

95-9 

99-7 

12 

54-  ' 

58.0 

61.8 

65.7 

69-6 

73-4 

81.2 

85.0 

88.9 

92.8 

96.6 

100.5 

13 

54-  S 

58.4 

62.3 

66.2 

70.1 

74.0 

81.8 

85-7 

89.6 

93-5 

97-4 

101.  2 

>4 

54-9 

58.8 

62.8 

66.7 

70.6 

74-5 

82.4 

86.3 

90.2 

94-  ' 

98.1 

102.  O 

IS 

55-3 

59-3 

63.2 

67.2 

,   , 

75-  I 

83.0 

86.9 

90.9 

94-8 

98.8 

02.7 

16 

55-7 

59-7 

63.7 

67-7 

I-  7 

75-6 

83.6 

87.6 

91.6 

95-5 

99-5 

03.5 

17 

56.  I 
56.5 

6a6 

64.6 

68.7 

2.7 

76.7 

84.8 

88.9 

92.9 

96.9 

IOI.O 

05  o 

'9 

56.9 

61.0 

65.1 

69.2 

3-2 

77-3 

85.4 

89-5 

93-6 

97-6 

101.7 

05.8 

20 

57-4 

61.5 

65.6 

69.6 

3-7 

77-8 

86.0 

90.1 

94.2 

98.3 

102.4 

06.5' 

21 

57.8 

61.9 

66.0 

70.  I 

4-3 

78.4 

86.6 

90.8 

94-9 

99-o 

103.2 

07  3  . 

22 

58.2 

62.3 

66.5 

70.  6 

4.8 

78.9 

87.3 

91.4 

95-6 

99-7 

'03  9 

08.0 

»3 

58.6 

62.8 

66.9 

71.  I 

5-3 

79-5 

87.9 

92.0 

96.2 

100.4 

104.6 

08.8 

24 

59-0 

63.2 

67-4 

71.6 

75-8 

80.0 

88.5 

92.7 

96.9 

101.  I 

105.  3 

09.5 

25 

59-4 

63.6 

67.9 

72.  I 

76.4 

80.6 

89.1 

93-3 

97-6 

101.8 

1  06.0 

10.3 

26 

59-8 

64-1 

68.3 

72.6 

76.9 

81.  i 

89.7 

94.0 

98.2 

102.  5 

106.8 

27 

60.2 

64.5 

68.8 

73-  i 

77-4 

81.7 

9°-3 

94.6 

98.9 

103.  2 

107.5 

it.  8 

28 

60.6 

64-9 

69-3 

73-6 

77-9 

82.2 

90.  9 

95-3 

99-6 

103-9 

108.  2 

12.5 

29 

61  0 

65.4 

69-7 

74-t 

78.4 

82.8 

9'-  5 

95-9 

100.  2 

104.6 

109.0 

'3-3 

3° 

61   4 

65.8 

70.2 

74-6 

79-0 

83-3 

92.1 

96-5 

00.9 

•'05.  3 

109.7 

14.  i 

31 

61.8 

66.2 

70.6 

75-  I 

79-5 

83-9 

92-7 

97-  « 

01.6 

106.0 

10.4 

14.8 

3* 

62.  2 

66.7 

71.  I 

75-6 

80.0 

84.  4 

93-3 

97-8 

O2.  2 

106.7 

II.  I 

15-6 

33 

62.6 

67   I 

71.6 

76.0 

80.5 

85-0 

93-9 

98.4 

02.9 

107.4 

ii.  8 

16.3 

34 

63.0 

67.5 

72.0 

76.5 

81.0 

85-5 

94.6 

99-  l 

03.6 

108.  I 

12.6 

17.1 

35 

63.4 

68.0 

72.5 

77-' 

81.6 

86.  I 

95-2 

99-7 

04.2 

108.8 

13-3 

17.8 

3* 

63.8 

68.4 

73-0 

77-5 

86.7 

95-8 

100.  3 

04.9 

109-5 

14.0 

18.6 

37 

64.2 

68.8 

73-4 

78.0 

82  6 

87.2 

96.4 

IOI.O 

05.6 

I    0.  I 

«4-7 

"9-3 

38 

64.7 

69-3 

73-9 

78.5 

83.1 

87.8 

97.0 

toi.6 

06.2 

i  0.9 

'5-5 

20.  I 

39 

65.' 

69-7 

74-4 

79.0 

83.7 

88.3 

97-6 

102.2 

06.9 

i   1.5 

16.  2 

20.  8 

4P 

65.5 

70.  I 

74-8 

79-5 

84.2 

88.9 

98.2 

102.  9' 

07.6 

I    2.  2 

16.9 

21.6 

4' 

65.9 

70.6 

75-3 

80.0 

84-7 

89.4 

98.8 

103.5 

08.2 

I    2.9 

17.6 

22.3 

42 

66.3 

71.0 

75-8 

80.5 

85.2 

90.0 

99-4 

104.2 

08.9 

i  3-6 

18.4 

ts 

43 

66.  7 

67  1 

7'.  4 
71-9 

76.  3 

76.7 

8i'.5 

85-  7 

86.3 

9°-  5 
91.1 

100.6 

105.4 

10.  2 

I  5-0 

19.8 

24.6 

45 

67.5 

67.  9 

72.3 
72.8 

77  > 
77-6 

82.0 
82.4 

as.  s 
87.3 

91.6 
92.2 

101.  2 

101.8 

I06.I 
106.7 

0.9 

'  5-7 

20.5 

25-3 
26.1 

46 
47 

68.3 
68.7 

73-2 
73-6 

78., 
78-5 

82.9 
83.4 

87.8 
88.3 

92.7 
93-2 

103.  I 

107.3 
108.0 

2-9 

I  7-8 

22.  7 

26.8 
27.6 

48 
49 

69.1 

74-1 

79.0" 

83-9, 

88.9 

93-8 

103-7 

108.6 

3-6 

118.  5 

23-4 

28.  4  : 

50 

69.5 

74-5 

79-5 

84-4 

89.4 

94-3 

104.3 

109.3 

4-2 

ii9.» 

24.2 

29.  1  j 

S« 

69  9 

74-9 

79-9 

84.9 

89.9 

94-9 

104.9 

109.9 

4-9 

119.9 

24-9 

29.9 

5* 

70.3 

75-4 

80.4 

85.4 

90.4 

<*' 

105.5 

II0.5 

5-6 

120.6 

25-6 

30.6; 

t*l      A 

S3 

70.  7 
71-  I 

75-  8 
76.2 

8K  3 

85-9 
86.4 

90.9 
9«-5 

96.6 

106.7 

in.  8 

6^9 

121.3 

122.  O 

26.  3 

27.0 

3~-  4  ' 

32.1 

54 
55 

71-5 

76.7 

81.8 

86.9 

92.0 

97-1 

107.3 

112.4 

7-5 

122.6 

27.8 

32.9 

56 

71.9 

77-  I 

82.2 

87.4 

92.5 

97-7 

107.9 

113.1 

8.2 

>23-3 

28.5 

33-6 

57 

7*-4 

77-5 

82.  7 

87.9 

93-0 

98.2 

108.5 

"3-7 

8.9 

124.0 

29.2 

34-4 

S« 

72.8 

78.0 

83-2 

88.4 

93-6 

98.7 

109.1 

"4-3 

9-5 

124-7 

29-9 

35-' 

59 

1397 

1497 

"597 

1697 

1797 

1896 

2096 

210 

2296 

2395 

2495 

2595 

Hon. 
Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .025  ft.  to  each   100  ft.  of 
distance  for  each  10'  departure. 


72 


TOPOGRAPHIC  STADIA   SURVEYING 


TABLE  7 — Continued 

DIFFERENCES    IN    ELEVATION 
3° 


t 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

5-23 

10.46 

15-68 

20.9 

26.1 

3«-4 

36.6 

4' 

47.0 

57-5 

62.7 

67-9 

5.^6 

10.51 

15-77 

21.0 

26.3 

31-5 

36.8 

42- 

47-3 

57-8 

63.1 

68.3 

5-^9 

10.  57 

15-85 

'll.  I 

26.4 

31-7 

37-o 

42. 

47-6 

58.1 

63-4 

68.7 

5-31 

10.  63 

15-94 

21.3 

26.6 

3'-9 

37-2 

42. 

47  8 

58.4 

63.8 

69.1 

5-34 

10.68 

16.03 

21.4 

26.7 

32.0 

37  4 

42 

48.1 

58-7 

64.1 

69.4 

5-37 

I0'74 

i6..u 

31.5 

26.9 

32.2 

37  6 

43- 

48.3 

59-  i 

64.4 

69.8 

5-40 

19.80 

16.20 

ti  6 

27.0 

3*-4 

378 

43-2 

48.6 

59-4 

64.8 

70.2 

5-43 

10.  86 

16.29 

21.7 

27  i 

32-6 

38.0 

43-4 

48.9 

59-7 

65.1 

70.6 

5.46 

10.92 

16-37 

21.8 

27-3 

32  7 

38.2 

43-7 

49-1 

60.0 

65-5 

71.0 

5-49 

10.97 

16.46 

21  .9 

27-4 

32  9 

384 

43-9 

49-4 

60.4 

65-8 

7i.  3 

1 

5-5* 

11.03 

16-55 

22.  1 

27.6 

33-  « 

38.6 

44-  I 

49-6 

60.7 

66.2 

71.7 

,1 

5-54 

II  IO 

16.63 

22.  2 

27-7 

33-3 

38.8 

44-4 

49-9 

61  o 

66.5 

72.  i 

1} 

5  58 

11.15 

16.72 

22-3 

27  9 

33-4 

39  o 

44-6 

50.2 

61.3 

66.9 

72.5 

3 

5.60 

It.  2O 

16.  81 

22  4 

28.0 

336 

39-2 

44-8 

50  4 

61.6 

67.2 

72.8 

4 

5  63 

11.26 

16.89 

22-5 

28.2 

33-8 

39  4 

45  o 

50  7 

61  9 

67.6 

73-2 

5 

5-66 

11.32 

16.98 

22.6 

28.3 

34  o 

39-6 

45  3 

50.9 

62.3 

679 

73-6 

6 

5.69 

..38 

17  07 

22.8 

28.4 

34  l 

398 

45-5 

Si  2 

62.6 

68  3 

74  o 

7 

5-72 

11.44 

'7-iS 

22  9 

28.6 

34-3 

40  o 

45-7 

5"  5 

62  9 

68.6 

74-3 

8 

5-75 

11.49 

17.24 

23.0 

28.7 

34-5 

40.2 

46  o 

Si  7 

63.2 

69.0 

74  7 

9 

5-77 

"•55 

'7-33 

23-  1 

28.9 

34  7 

40.  4 

46  2 

52-0 

63.5 

693 

75  ' 

JO 

5.8o 

11.61 

17.41 

23.2 

29.0 

34-8 

40  6 

46.4 

52.2 

63.8 

69.6 

75  5 

21 

5-83 

11.67 

17  SO 

23  3 

29-  J 

35  o 

40.8 

46.7 

52  5 

64.2 

70  o 

75  8 

22 

5-86 

11.72 

"7-59 

23-4 

29-3 

35  2 

4  0 

46.9 

52.8 

64-5 

70.4 

76.2 

23 

5  89 

n  78 

17  67 

23.6 

29  5 

35-3 

4  2 

47  i 

53  o 

64.8 

70.7 

76  6 

24 

5  9J 

it  84 

17  76 

23  7 

296 

35  5 

4  4 

47  4 

53-3 

65.1 

71  o 

77  0 

25 

5  95 

11.90 

17  85 

238 

29  7 

35  7 

4  6 

47  6 

53  5 

654 

71  4 

77  3 

26 

598 

n  96 

'7  93 

23  9 

29  9 

35  9 

4  8 

478 

53-8 

65.8 

71  7 

77  7 

27 

6  01 

12  Ol 

18.02 

24.0 

30  o 

36.0 

4  0 

48.1 

54-  l 

66.1 

72  1 

7».i 

28 

6.04 

12  O7 

18.  n 

24  i 

30  2 

36  2 

4  2 

483 

54  3 

66.4 

72  4 

73-5 

29 

6.06 

12.  13 

18  19 

24  3 

30  3 

36  4 

4  4 

48  5 

54  6 

66  7 

72  8 

78.8 

30 

6  09 

12  19 

18  28 

24  4 

30  5 

36  6 

4  7 

48.7 

54-8 

67  o 

73-  « 

79-  » 

3« 

6  12 

12  24 

18.37 

»4  5 

306 

367 

42  9 

49  o 

55-  « 

67  3 

73-5 

79-6 

3* 

6.15 

12  30 

18.45 

24  6 

308 

36  9 

43  ' 

49  2 

55  4 

67  7 

73-8 

80.0 

33 

6  18 

12  36 

18.54 

24  7 

30  9 

37  i 

43  3 

49  4 

55  6 

68  o 

74-2 

80.3 

34 

6  21 

12.42 

.863 

24.8 

3'  o 

37  2 

43  5 

49  7 

55-9 

68  3 

74-5 

80.7 

35 

6  24 

12.48 

187' 

25.0 

31  2 

37  4 

43  7 

49  9 

56  i 

68.6 

74--9 

81  l 

36 

6.27 

12.53 

18  80 

25  ' 

3'  3 

376 

43  9 

50.  i 

56-4 

689 

75-'2 

81.5 

37 

6.30 

12.59 

18  89 

25.2 

3i  5 

37  8 

44-  i 

50  4 

56.7 

69.2 

75  5 

81.8 

38 

6  32 

12  65 

1897 

25  3 

3'  6 

37  9 

44  3 

506 

56  9 

69.6 

75-9 

82.2 

39 

6-35 

12.71 

19.06 

25  4 

3'  8 

38.1 

44  5 

50  8 

57  2 

69.9 

76.2 

82.6 

40 

6.38 

12  76 

19-  15 

25-5 

3«  9 

38.3 

44-7 

5'  i 

57  4 

70  2 

76.6 

83-0 

4' 

6.41 

12.82 

19-23 

25  6 

32.1 

38  5 

44  9 

5'  3 

57  7 

70  5 

769 

83-3 

42 

6.44 

12  88 

19  32 

25.8 

32-2 

386 

45  i 

5'  5 

580 

70.8 

77  3 

83-7 

43 

647 

12.94 

19.41 

25  9 

32-3 

38.8 

45  3 

5'  7 

58  2 

7'  i 

77  6 

84.1 

44 

6  50 

13.00 

19  49 

26.0 

32.5 

39-o 

45  5 

52.0 

58.5 

7'  5 

78.0 

84-5 

45 

6.53 

13.05 

•958 

26.1 

32.6 

39-2 

45  7 

52  2 

58.7 

7i  8 

78.3 

84.8 

46 

6.56 

13  11 

19.66 

26  2 

32  8 

39  3 

45  9 

52  4 

59  o 

72  i 

78  7 

85.2 

47 

6.59 

'3  «7 

"9-75 

26  3 

32  9 

39  5 

46  i 

52  7 

59-3 

72  4 

79-o 

85.6 

48 

6.61 

•3  23 

19.84 

26.4 

33-1 

39-7 

46.3 

52.9 

59-5 

72  7 

79-4 

86  o 

49 

6.64 

•  3-28 

19.92 

26.6 

33-2 

39.8 

465 

53-  i 

59-8 

73-  ' 

79-7 

86.3 

50 

6.67 

«3-34 

20.01 

26.7 

33  4 

40.0 

46.7 

53  4 

60.0 

73  4 

80.0 

86  7 

5' 

6.70 

'3-40 

2O.  IO 

26.8 

33-5 

40.2 

46.9 

53  6, 

60.3 

73  7 

804 

87.1 

52 

6  73 

'3-46 

20.  1  8 

26.9 

33-6 

40.4 

47  > 

53  8 

60.6 

74  o 

80  7 

87  5 

53 

6.76 

'3  5' 

20.  27 

27  o 

33-8 

40  5 

47  3 

54  i 

60.8 

74  3 

81  i 

87.8 

54 

6.79 

'3-57 

20.36 

27  i 

33-9 

40.7 

47  5 

54-3 

61.  i 

74.6 

81  4 

88.2 

55 

6.81 

>3-63 

20.44 

27  3 

34-  » 

40.9 

47  7 

54-5 

61  3 

75  o 

81  8 

88.6 

56 

«7 

6.85 
6.  88 

•3-69 

20.53 

27-4 

34-2 

41.  i 

47  9 

54  7 

61  6 

75  3 

•7C  f\ 

82.1 

g2  5 

89-0 

flrt  i 

58 

6^90 

13-80 

20.70 

27  61 

34  5 

41  4 

48  3 

55  2 

62  i 

75  ° 
75  9 

82  8 

*»9-  3 

89-7 

59 

6.93 

13.86 

20.79 

27-7 

34  6 

41.6 

48.5 

55-4 

62.4 

76.2 

83-2 

90.  i 

Horz. 
Dist. 

99-63 

'99-3 

298.9 

398.5 

498.2 

598 

697 

797 

897 

1096 

1196 

1295 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .035  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


73 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
3° 


1400 

1500 

1600 

1700 

1800 

1900 

2100 

2200 

2300 

2400 

2500 

2600 

f 

73-2 

78.4 

83.6 

88.8 

94.1 

99-3 

09.8 

"5-o 

I2O  2 

125-4 

130.7 

«35-9 

O 

73-6 
74.0 

78.8 
79-3 

84.. 
84.6 

SI 

94.6 
95-1 

99-9 
loo.  4 

10.4 

"5.6 
16.3 

120.9 
121.  5 

126.1 
126.8 

131-4 
132.1 

136.6, 
137-4 

2 

74-4 
74.  8 

79-7 
80.  i 

85-0 
85.  5 

90.4 
90.8 

95-6 

100.9 

ii.  6 

16.9 

122.  2 

127-5 

132.  8 

138.  «  . 
138.9 

3 

4 

75-  2 
75-6 

80.6 
81  o 

85.9 
86.4 

91-3 

91.8 

96.7 
97.1 

O2.  6 

13-4 

18.  8 

124.3 

128.9 
129.6 

134-3 
'35-o 

«39-6 
140.4 

5 
6 

76.0 

81.4 

86.9 

92.3 

97-7 

03.2 

14.0 

19.4 

124.9 

'30-3 

'35-7 

141.2 

7 

76.4 

81.9 

87  3 

92.8 

98.2 

03-7 

14.6 

.25-5 

131-0' 

136.4 

141-9 

8 

76.  8 

77  * 

82.3 
82  7 

88.2 

93-8 

99-3 

04-9 

15.8 

21.3 

126.9 

132-4 

"37-9 

"43-4 

10 

77  6 

83.2 

88.7 

94-  3 

99-8 

05-3 

16.4 

22.  O 

'27-5 

'33-  i 

138,6 

144.2 

i 

78.0 

83.6 

89.2 

94-7 

100.  3 

05-9 

22.6 

128.2 

•33-8 

139-3 

144.9 

2 

78.4 

84.0 

89.6 

95-2 

loo.  8 

06.4 

17^6 

23-3 

128.9 

'34-5 

140.  i 

'45-7 

J 

78.8 

84-5 

90.  i 

95-7 

01.  4 

07.0 

18.3 

23.9 

'29-5 

135-2 

140.8 

146-4 

4 

79.2 

84.9 

90.6 

96.2 

01.9 

07.5 

18.9 

24-5 

130.2 

'35-8 

141-5 

147-2 

5 

79  .6 

8S-3 

91  o 

96.7 

02.4 

08.  I 

'9-5 

25-2 

130.8 

136.5 

142.  2 

147-9 

6 

80.0 

862 

9"-5 

97-2 

02.  9 

08.6 

20.  I 

25-8 

'3'-5 

•137.2 

143-0 

148.7 

7 
18 

80.5 
80.  9 

86^6 

92  o 
92.4 

98  2 

04.0 

09.7 

21-3 

27.1 

132-9 

137.  9 
138.6 

'43-  7 
144.4 

150.2 

'9 

81.3 

87  i 

92  9 

98.7 

04.4 

to.  3 

21.9 

27-7 

133-5 

'39-  3 

'45-1 

150-9 

20 

8.  7 

87  5 

93  3 

99  2 

05.0 

10.8 

22.5 

28.3 

134-2 

140.0 

145.8 

«5'-7 

21 

82  i 
82  5 

III 

93-8 
94  3 

99-7 

05  5 
06.0 

II.  4 
"9 

23.  ' 
23.7 

29.0 
29.6 

'34-9 
'35-5 

140.7 

146.6 

•52-4 

22 

82  9 

83  3 

88.8 
89  2 

94  7 
95  2 

100.6 

07  ' 

'3  o 

24.9 

30.9 

136.8 

142.7 

148.7 

'53-9 
'54-7 

24 
25 

837 
84  I 

89  7 
90  i 

95  & 
96.  1 

ioi  6 

102  I 

07  6 
08  i 

'36 

25.5 

3'  5 

'37  5 

'43-  5 

149.4 

155-4 

26 

27 
28 

84  5 
84  9 
85  3 

90  5 
91  4 

96  6 
97  5 

IO2  6 

103.  6 

09.7 

5-8 

33-4 

34-  i 

138.  8 
'39-5 
140.2 

144.  8 
'45  5 
146.2 

'5°-  9 
151  6 
152-3 

156-  9 
'57  7 
'584 

29 

30 

85  7 

9.  8 

98.0 

104  I 

0  2 

63 

28.6 

34-7 

140.8 

146.9 

1  53-  i 

'59-2 

3' 

86  i 

92  3 

98.4 

104.  6 

07 

6.9 

29.  2 

35  3 

14'  5 

147  6 

'53.8 

'59-9 
1  60.  7 

32 
33 

86.  5 
86.9 

Q_   , 

92  7 
93  ' 

98.  9 
99  3 
nn  8 

105.  6 

i  8 

8.0 

30  4 

366 

142  8 

149.0 

155-2 
156.  o 

161.4 

l62.  2 

34 
35 

B7  3 
87  7 

93-  6 
94  o 

99-  " 

oo.  3 

106  5 

2  8 

'9  ' 

3'  6 

37  9 

'43*  5 
144-  1 

'5°-4 

156  7 

162.9 

36 

88.  i 

94  4 

00.7 

107.0 

3  3 

19.6 

32  2 

38.5 

144.8 

IS'-' 

157-4 

163  7 

37 

88  5 

94  8 

01  2 

'07  5 

38 

20  2 

32-8 

39  i 

145-5 

•  5'.  8 

158-1 

164.4 

38 

889 

95-3 

01  6 

108.0 

4-  4 

20.  7 

33-4 

39-8 

146.1 

152.5 

158.8 

.65.2 

39 

89.4 

95  7 

02  1 

108.5 

49 

21  3 

34-0 

40.4 

146.8 

153-2 

•59-6 

165-9 

40 

89.7 

96  2 

02  6 

109.0' 

5-4 

21  8 

34-6 

41.0 

147-4 

'53-9 

160.3 

166.7 

4' 

90  2 

96.6 

03.0 

'09-5 

5-9 

22  4 

35-2 

4i  7 

148.1 

154.6 

161.0 

167.4 

4* 

90.6 

97  o 

03-5 

I  !0  0 

64 

22  9 

35-8 

42.3 

148.8 

155-2 

161.7 

168.2 

43 

97  5 

04.0 

MO  5 

7  o 

23  5 

36.4 

42.9 
.,  f. 

149.4 

I55.9 
T*j6  6 

162.4 

I  f,  I   2 

168.9 
169.  7 

44 
45 

91  4 
9,  8 

97  9 
98  3 

04.  4 
04.9 

III  4 

80 

24  5 

37-  i 
37  7 

43-  ° 
44-  2 

150.  i 
150.8 

157  3 

lOj.  2 

163.9 

170.4 

46 

92  2 

98  8 

05  3 

in  9 

85 

25-  ' 

38.3 

44-8 

151-4 

158.0 

164.  6 

171.2 

47 

92  6 

99  2 

05  8 

112  4 

9  o 

25.6 

38.9 

45-5 

152.1 

158-7 

165.3 

171.9 

48 

93  0 

99  6 

06  3 

112  9 

9  5 

26  2 

39-5 

46.1 

152-7 

'59-4 

166.0 

172.7 

49 

93  4 

100.  1 

06.7 

"3-4 

0  I 

26.7 

40.1 

46.8 

153-4 

160.  i 

166.8 

•73-4 

5» 

93  « 

oo  5 

07  2 

"39 

o  6 

27  3 

40  7 

47-4 

'54-  i 

160.8 

•67-5 

174.2 

5« 

94  2 

07  6 

"44 

i  i 

27  8 

4'  3 

48.0 

'54-7 

161.5 

168.2 

174-9 

5* 

94-6 

01  4 

08  i 

114.9 

i  6 

28  4 

41.9 

48.6 

'55-4 

162.2 

168.9 

175-7 

53 

95-0 

01  8 

08  6 

"5-4 

2.  I 

28.9 

42.5 

49-3 

156.1 

162.9 

169.6 

176.4 

54 

95  4 

02  I 

09.0 

"5.8 

2  7 

29-5 

43-  ' 

49-9 

156.7 

'63.5 

170.4 

177.2 

55 

05.8 

02  6 

09.5 

U6.3 

3-2 

30.0 

43-7 

50.6 

157-4 

164.2 

171.  I 

177.9 

56 

96  2 

03  1 

09.  9 

116.8 

3-7 

30.6 

44-3 

5'-2 

158.1 

164.9 

171.8 

178.7 

57 

96.6 

°3  5 

10  4 

"73 

4-2 

3'  ' 

44-9 

5'.  8 

•58.7 

165.6 

172.5 

179-4 

5» 

97  O 

04.0 

10.  9 

117.8 

4-7 

3'  7 

45-5 

52.5 

'59-4 

166.3 

173  3 

1  80.  2 

59 

'395 

1494 

'594 

1694 

'793 

•893 

2092 

Horz. 
Disc 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .035  ft.  to  each   100  ft.  of 
distance  for  each  10'  departure. 


74 


TOPOGRAPHIC   STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 
4° 


/ 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

0 

6.96 

'3-  92 

20.87 

27  8 

34-8 

41.8 

48-7 

55-7 

62.6 

76-5 

83.5 

90-5 

6.99 

13-98 

20.96 

28.0 

34-9 

41.9 

48.9 

55-9 

62.9 

76.9 

83-8 

90.8 

3 

"4-03 

21.05 

28.  i 

35-  i 

42.1 

49-  ' 

56.1 
56.  4 

63.  i 

77-  2 

84.2 
84-  5 

91-2 
91.  6 

3 
4 

7-  °5 

7.08 

14.  09 
I4-15 

21.  22 

28.3 

35-4 

42.  4 

49-5 

56.6 

63-7 

77-8 

84.9 

92.0 

S 

7.10 

14.21 

21.31 

28.4 

35-5 

42.6 

49-7 

56.8 

63-9 

78.1 

85.2 

92-3 

6 

•  "3 

14.  26- 

21-39 

28.5 

35-7 

42.8 

49-9 

57-1 

64.  2 

78.4 

85.6 

92-7 

7 

.  16 

14.32 

21.48 

28.6 

35-8 

43-0 

50-  i 

57-3 

64.  4 

78.8 

85-9 

93-  I 

8 

•  19 

I4-38 

21-57 

28.8 

35-9 

43-  i 

50-3 

57-5 

64-7 

79-  I 

86.3 

93-5 

9 

14.44 

21.65 

28.9 

36-1 

43-3 

50-5 

57-7 

65.  o 

79-4 

86.6 

93-8 

10 

•25 

14.49 

21-74 

29.0 

36.2 

43-5 

50-7 

58.0 

65.  2 

79-7 

87.0 

94-2 

II 

.28 

'4-  55 

21.83 

29.  I 

36-4 

43-7 

50-9 

58-2 

65-5 

80.0 

87-3 

94-6 

12 

3° 

14.61 

21.91 

29.2 

36-5 

43-8 

5'-  i 

58-4 

65.  7 

80.3 

87.6 

95-0 

13 

•  33 

14.67 

22.00 

29-3 

36.7 

44-0 

51-3 

58.7 

66.0 

80.7 

88.0 

95-3 

14 

.36 

I4-72 

22.08 

29.4 

36-8 

44-2 

Si-5 

58-9 

66.3 

81.0 

88.3 

95-7 

'5 

•39 

14.78 

22.17 

29.6 

37-o 

44-3 

51-7 

59-  i 

66.  5 

81.3 

88.7 

96.1 

16 

•42 

14.84 

22.26 

29.7 

37-1 

44-5 

51-9 

59-4 

66.8 

81.6 

89.0 

96.4 

06  8 

17 
18 

:Ji 

14.  90 
14-95 

22.  34 

22.43 

29.  8 
29-9 

37-  2 
37-4 

44-9 

52-3 

59-8 

67-3 

82.  2 

89.7 

90.  o 
97-2 

>9 

7.51 

i5-<" 

22.  52 

30.0 

37-5 

45-0 

52-5 

60.  o 

67-5 

82.6 

90.  i 

97-6 

20 

7-53 

15-07 

22.60 

30.1 

37-7 

45-2 

52-7 

60.3 

67.8 

82.9 

90.4 

97-9 

2, 

7-56 

I5-I3 

22.69 

30-3 

37.8 

45-4 

52-9 

60.5 

68.  i 

83-2 

90.8 

98-3 

22 

7-59 

I5--8 

22.78 

30.4 

38-0 

45-6 

53-1 

60.7 

68.3 

83-5 

91.  i 

98.7 

23 

7.62 

"5-24 

22.86 

30-5 

38.1 

45-7 

53-3 

.0 

68.6 

83-8 

91.  4 

99-  I 

24 

7.65 

'5-3° 

22.95 

30.6 

38-2 

45-9 

53-5 

.  2 

68.8 

84.I 

91.8 

99-4 

25 

7.68 

15-36 

23-03 

30-7 

38-4 

46.1 

53-7 

•  4 

69.  i 

84-5 

92.  i 

99-8 

26 

7.71 

15-4I 

23.12 

30-8 

38.5 

6.2 

53-9 

•7 

69.4 

84.8 

92.5 

100.  2 

27 

7-74 

'5-47 

23.21 

30-  9 

38-7 

6.4 

54-  i 

.  9 

69.  6 

85-1 

92.8 

ioo.  6 

28 

7.76 

15-53 

23-29 

3  -i 

38-8 

6.6 

54-4 

2.  1 

69.9 

85-4 

93-2 

100.9 

29 

7-79 

15-59 

23-38 

3  -2 

39-0 

6.8 

54-6 

2-3 

70.  i 

85-7 

93-5 

101.3 

3° 

7.82 

15-64 

23-46 

3  -3 

39-  I 

6-9 

54-8 

2.6 

70.4 

86.0 

93-9 

101.7 

31 

7.85 

15-70 

23-55 

3  -4 

39-3 

7-  i 

55-o 

62.8 

70.7 

86.4 

94-2 

102.  I 

32 

7.88 

15-76 

23-64 

3  -5 

39-4 

7-3 

55-2 

63.0 

70.9 

86.7 

94-5 

102.4 

33 

7.91 

15-  82 

23-72 

3  -6 

39-5 

7-4 

55-4 

63.3 

71.  2 

87.0 

94-9 

102.8 

34 

7-94 

15-87 

23.81 

3  -7 

39-7 

47.6 

55-6 

63.5 

71-4 

87-3 

95-2 

103.  2 

35 

7-97 

15-93 

23.90 

3  -9 

39-8 

47-8 

55-8 

63.7 

71-7 

87.6 

95-6 

103.  6 

36 

7-99 

15-99 

23-98 

3  -o 

40.  o 

48.0 

56.0 

64.0 

7»-9 

87-9 

95-9 

103.9 

37 

8.02 

16.05 

24.07 

3  •  i 

40.  i 

48.1 

56.2 

64.2 

72-  2 

88.2 

96-3 

104.3 

38 

8.05 
8.08 

16.  10 

24-15 

3  -2 

40.3 

48-3 

AQ     c 

56-4 
56  6 

64.4 

64.  6 

72.5 

88.6 
88  9 

96.  6 

104.  7 

39 
40 

8.  ii 

16.22 

24-  33 

3  -4 

40.5 

40-  5 
48.7 

.0    O 

56^8 

64.9 

Ar     i 

73-o 

s9:2 

gg     e 

97-3 

"05-4 
105.8 

42 
43 

8.17 

8.20 

•6.33 
16.39 

24-50 
24.58 

1:1 

40.8 
41.0 

40.  o 

49.0 

49.2 

57-  o 
57-2 
57-4 

05.  1 

65-3 
65.6 

73-  2 
73-5 
73-8 

89^8 

90.  1 

98!  o 
98-3 

106.2 
106.5 

44 

8.22 

16-45 

24.67 

3  -9 

41.  i 

49-3 

57-6 

65.8 

74-o 

90-5 

98-7 

106.9 

45 

8.25 

.6.50 

24-76 

33-o 

4i-3 

49-5 

57-8 

66.0 

74-3 

90.8 

99.0 

107.3 

46 

8.28 

16.56 

24.84 

33-' 

41.4 

49-7 

58.0 

66.2 

74-5 

91.1 

99-4 

107-7 

47 

8.31 

16.62 

24-  93 

33-  2 

1.6 

49-9 

58-2 

66.5 

74-8 

91.4 

99-7 

48 

8-34 

16.68 

25.02 

33-4 

i-7 

50.0 

58-4 

66.7 

75-o 

91-7 

00.  I 

I08.'4 

49 

8.37 

16-73 

25.10 

33-5 

1.8 

50.2 

58-6 

66.9 

75-3 

92.0 

00.4 

108.8 

SO 

8.40 

16.79 

25-  19 

33-6 

2.0 

50.4 

58.8 

67.2 

75-6 

92-4 

00.8 

109.1 

5> 

8-43 

16.85 

25-27 

33-7 

2.  I 

50.5 

59-0 

67-4 

75-8 

92.7 

01.  I 

109-5 

52 

8-45 

16.91 

25-36 

33-8 

'.3 

50-7 

59-2 

67.6 

76.1 

93-o 

01.  4 

109.9 

53 

8.48 

16.96 

25-45 

33-9 

2.4 

50-9 

59-4 

67-9 

76-3 

93-3 

01.  8 

110.3 

54 

8.51 

17.02 

25-  53 

34-0 

2.6 

51-  ' 

59-6 

68.  I 

76.6 

93-6 

02.  i 

1  10.  6 

55 

8-54 

.7.08 

25-62 

34-2 

42.7 

51-2 

59-8 

68.3 

76.9 

94-9 

02.5 

III.O 

56 

8-57 

17.14 

25-70 

34-3 

42.8 

51-4 

60.0 

68.5 

77-1 

94.2 

02.8 

1  1  1.  4 

57 

8.60 

17.  19 

25-79 

34-4 

43-o 

51-6 

60.  2 

68.8 

77-4 

94-6 

03.2 

in.  8 

58 

8.63 

17-26 

25-87 

34-5 

43-1 

5  -8 

60.4 

69.0 

77.6 

94-9 

03-5 

1  12.  I 

59 

8.65 

I7-3I 

25.96 

34-6 

43-3 

5i-9 

60.6 

69-2 

77-9 

95-2 

03.8 

112.5 

Horz. 
Dist. 

99-38 

98.8 

298.  I 

397-5 

496.9 

596 

696 

mj 

894 

1093 

"93 

1292 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .045  ft.  to  each  ioo  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


75 


TABLE  7 — Continued 

DIFFERENCES  IN   ELEVATION 


1400 

1500 

1600 

1700 

1800 

1900 

2100 

2200 

2300 

™ 

2500 

2600 

f 

97- 

04.4 

1-3 

18.3 

125.2 

32-2 

146.1 

153-1 

1  60.  o 

167.0 

174.0 

,80.9 

O 

97- 

04.8 

1.8 

18.8 

125.8 

32.8 

146.7 

153-7 

160.7 

167-7 

174-7 

181.7 

1 

98. 

05.2 

2-3 

19-3 

126.3 

33'  3 

147-3 

154-4 

161.4 

168.4 

175-4 

,82.4 

1 

98. 

05-7 

2-  7 

19.8 

126.8 

33-9 

'47-9 

155-0 

162.  o 

169.  i 

176.1 

183.2 

3 

99- 

06.  i 

3-2 

20.  3 

127-3 

34-4 

148.6 

155-6 

162.7 

169.8 

176.8 

•83-9 

4 

99- 

06.5 

3-6 

20.7 

127.8 

34-9 

149-2 

156.3 

163.4 

170-5 

177.6 

184.7 

5 

99- 

07.0 

4.1 

21.  2 

128.4 

35-5 

149-8 

156.9 

164.0 

171.2 

•78-3 

185.4 

6 

00. 

07.4 

4-6 

21.  7 

128.9 

36.0 

150.4 

157-5 

164.7 

171.8 

179.0 

186.2 

7 

oo.  » 

07.8 

5-o 

22.  2 

129.4 

36.6 

151-0 

•  58.2 

165.3 

I72-5 

"79-7 

186.9 

8 

01. 

08.3 

5-5 

22.  7 

129.9 

37-1 

15'-  6 

158.8 

166.0 

173-2 

1  80.  4 

9 

01. 

08.7 

5-9 

23-2 

130.4 

37-7 

152.2 

159-4 

1  66.  7 

'73-9 

181.2 

\88.  4 

01. 

09.  i 

6.4 

23-7 

131-0 

38-2 

152.8 

160.  I 

167-3 

174.6 

181.9 

189.2 

,, 

02.  • 

09.6 

6.9 

24.2 

131-5 

38.8 

'53-4 

160.7 

168.0 

175-3 

182.6 

189.9 

12 

02. 

IO.  O 

7-3 

24.7 

132-0 

39-3 

"54-0 

161.  3 

168.7 

176.  o 

183-3 

190.7 

3 

OJ. 

10.4 

7.8 

25-  ' 

132-5 

39-9 

154-6 

162.0 

169-3 

176.7 

,84.0 

191.4 

4 

03-5 

10.  9 

8.2 

25.6 

'33-0 

40.4 

155-  2 

162.6 

470.  o 

177-4 

184.7 

192.2 

5 

03-9 

"•3 

8.7 

26.  1 

I33-S 

41.0 

155-8 

.6-3.2 

170.  6 

178.  i 

185-5 

192.9 

6 

°4-3 

11.7 

2 

26.6 

"34-  i 

1-5 

156-4 

163.9 

i   i-3 

178.8 

186.2 

193-  6 

7 

04.7 

12.  2 

6 

27.  I 

134-6 

2.  I 

157-0 

164.5 

i   2.9 

179-4 

186.9 

194.4 

18 

05.  I 

12.6 

I 

27.6 

'35-  ' 

2.6 

•  57.6 

165.  i 

1     2.6 

1  80.  i 

187.6 

195-  i 

19 

05-5 

13-0 

6 

'35-6 

3-2 

158.2 

165.8 

i   3-3 

180.8 

.  188.4 

'95-9 

05-9 

'3-4 

o 

28.6 

136.1 

3-7 

158.8 

166.4 

i   3-9 

181.5 

189., 

196.  6 

21 

06.3 

"3-9 

5 

29.  I 

'36.7 

4-2 

159-4 

167.0 

i   4.6 

182.  2 

189.8 

'97-4 

22 

06.7 

'4-3 

9 

29-5 

137.2 

4.8 

160.0 

167.6 

i   5-3 

182.9 

190.5 

23 

O?.  1 

14.7 

4 

30.0 

137-7 

5-3 

160.  6 

168.3 

i    5-9 

•83.6 

191.  2 

198.9 

24 

07-5 

'5-2 

8 

3°-5 

138.2 

5-9 

161.2 

168.9 

176.6 

184-3 

I92.O 

199.6 

25 

07.9 

nft    l 

15-6 

3 

g 

31-0 

138-7 

6.4 

161.8 

169.6 

177-3 

185.  o 

,QC     ~, 

192.7 

200.  4 

26 

os.  3 

08.7 

i6!5 

2 

31*  5 
32.0 

J39-8 

7-5 

163-1 

170.  8 

178.6 

105.  7 
186.3 

193-  4 
194-  1 

201.  9 

28 

09.  1 

16.9 

7 

32-5 

MO  3 

163-7 

171.4 

179.  2 

187.  o 

194-8 

2O2.  6 

29 

09-5 

17-3 

1 

33-o 

140.  8 

8^6 

164-3 

172.  i 

189.9 

187.7 

195-5 

203.4 

30 

09.9 

17.8 

25-6 

33-5 

I4I-3 

49-2 

164.9 

172.7 

180.6 

188.4 

196.3 

204.   1 

3' 

10.3 

18.  2 

26.  i 

33-9 

141.8 

49-7 

I&5-5 

173-3 

181.  2 

189.  i 

197.0 

204.9 

32 

10.  7 

18.6. 

26.5 

34-4 

142-3 

50-3 

1  66.  I 

174.  o 

181.9 

.89.8 

•97-7 

205.  6 

33 

u.  I 

19.  o 

27.0 

34-9 

142.9 

50.  8 

166.7 

174.  6 

182.5 

'90.5 

198.4 

206.  3 

34 

'1-5 

'9-5 

27-4 

35-4 

'43-4 

5'.3 

167-3 

175-2 

183.2 

.  Q,     0 

199.  I 
ion  ft 

207.  i 

35 
16 

12-3 

12.7 

20.3 

20.  8 

2!  4 
28.8 

35-  9 
36.4 
36-9 

144.4 
144.9 

52-4 
53  o 

168.5 
169.  i 

175-  9 
176-  5 
177.  i 

'°3-  9 
184-5 

185.  2 

192.  6 
193-2 

199.  o 
200.  6 

201.3 

208.  6 
209-3 

3° 
37 
38 

13-  i 

2    .  2 

29-3 

37-4 

"45-4 

53-5 

169.7 

177-8 

185-8 

193-9 

2IO.  1 

39 

"3-5 

2    .6 

29.7 

37-9 

146.9 

54-  ' 

170.3 

178.4 

I86.5 

194-6 

202.  7 

210.  8 

40 

'3-9 

2    .  I 

30.2 

38.3 

146.5 

54-6 

170.9 

179.0 

187.2 

195-3 

203.4 

211.  6 

4' 

'4-3 

2    -5 

30-7 

38.8 

147.0 

55-  2 

I7L5 

179.7 

187.8 

,96.0 

204.  2 

212.3 

42 

'4-7 

2    .9 

31-  l 

39-3 

'47-5 

55-7 

172.1 

1  80.  3 

188.5 

196.7 

204.9 

213.  1 

43 

'5-  ' 

23-4 

31-6 

39-8 

148.0 

56.2 

172.7 

1  80.  9 

189.1 

197-4 

205.  6 

213.  8 

44 

"5-5 

23-8 

32.0 

40.3 

'48.5 

56.8 

173-3 

181.6 

I89.8 

198., 
tnft   7 

206.  3 

214.6 

45 

46 

15.  9 
16.3 
16.7 

24-7 
25.1 

33-9 
33-4 

4'-3 
41-8 

149.6 
150.  i 

57-9 
58-4 

174-5 
175-  « 

182.8 
183-4 

190.  5 
191.  i 
191.8 

190.  7 
199.4 
200.  1 

207.  8 
208.  5 

216'  I 

216.8 

H 

17.  i 

25-5 

33-9 

42.  2 

150.6 

59-0 

•75-7 

184.1 

192.4 

200.  8 

209.  2 

217-5 

49 

'7-5 

25-9 

34-3 

42.7 

151-1 

59-5 

176.3 

184.7 

193-  « 
T_.   o 

201.  5 

209.9 

218.3 

50 

17.  9 
•  8.3 
18.7 

26.  4 
26.8 
27.2 

35-2 
35-7 

43-  2 

43-7 
44.2 

151.  6 

152.2 
.152.7 

60.6 
61.2 

176-  9 
'77-5 
178.1 

\S6o 
186.6 

193-  8 
194.  4 
195-  i 

202.9 

203.6 

211.3 

219.  8 

220.  5 

52 
5. 

19.  i 

27.7 

36.2 

44-7 

'53-  2 

61.  7 

178.7 

187.2 

195-7 

204.  2 

212.  8 

221.3 

54 

'9-5 

28.1 

36.6 

45-2 

'53-7 

62.2 

179-3 

•  87.9 

196.4 

204.  9 

213-5 

222    0 

55 

20.0 

28.5 

37-  I 

45-7 

'54-2 

62.8 

179-9 

188.5 

197-1 

205.  6 

214.  2 

222.8 

56 

20.4 

28.9 

37-5 

46.1 

«54-7 

63-3 

1  80.  5 

189.  i 

97-7 

206.  3 

214.  9 

223-5 

57 

20.8 

29-4 

38-0 

46.6 

155-2 

63-9 

181.1 

189.8 

198-4 

207.  o 

215.  6 

224-3 

58 

21.  2 

29.  8 

38-5 

47-  i 

J55-8 

64.4 

181.  7 

190.4 

199.0 

207.  7 

216.4 

225.0 

59 

1391 

1491 

'590 

1689 

•  789 

,888 

2087 

2186 

2286 

2385 

2484 

2584 

Horr. 
Dist. 

Hor.  dist.  is  for  3</  point.     Add  or  subtract  .045  ft.  to  each  100  ft.  of 
distance  for  each  jp'  departure. 


76 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 

5° 


' 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

0 

8.68 

7-36 

26.05 

34-7 

43-4 

52-1 

60.8 

69-5 

78.1 

95-5 

104.  3 

12.9 

1 

8.71 

7-42 

26.13 

34-8 

43-6 

52-3 

61.  o 

69.7 

78.4 

95.8 

104-5 

13-2 

2 

8.74 

7.48 

26.22 

•35-o 

43-7 

52-4 

61.2 

69.9 

78.7 

96.1 

104.9 

13-6 

3 

8.77 

7-54 

26.31 

35-  i 

43-8 

52-6 

61.4 

70.1 

78.9 

96.4 

105.2 

14.0 

4 

8.80 

7-59 

26.39 

35-2 

52.8 

61.6 

70.4 

79-2 

96.8 

105.6 

14.4 

5 

8.82 

7-65 

26.48 

35-3 

44.1 

53-o 

61.8 

70.6 

79-4 

97-  « 

105-9 

14-7 

6 

8.85 

7.71 

26.56 

35-4 

44-3 

53-1 

62.0 

70.8 

79-7 

97-4 

106.2 

15-  > 

7 

8.88 

7-77 

26.65 

35-5 

44-4 

53-3 

62.  2 

71.  r 

79-9 

97-7 

106.6 

15-5 

8 

8.9: 

7.82 

26.73 

35-6 

44-5 

53-5 

62.4 

7'-3 

80.2 

98.0 

106.9 

15-8 

9 

8.94 

7.88 

26.82 

35-8 

44-7" 

53  6 

62.6 

7i-5 

80.5 

98-3 

107-3 

16.  2 

10 

8.97 

7-94 

26.  90 

35-9 

44-8 

53-8 

62.8 

71.8 

80.7 

98-7 

107.6 

16.6 

12 

9.  oo 
9.03 

Is.  05 

26.  99 
27.08 

36.  o 
36-1 

44-  9 

45-" 

54-  ° 
54-2 

63.2 

2.  2 

81.2 

99-3 

108.3 

17-3 

13 

9.06 

18.  11 

27.16 

36-2 

45-3 

54-3 

63-4 

2.4 

81.5 

99-6 

108.7 

17-7 

14 

9.08 

18.17 

27.25 

36-3 

45-4 

54-5 

63-6 

2-7 

81.7 

99-9 

109.0 

18.  i 

15 

9.11 

l8.  22 

»7-33 

36-4 

45-6 

54-7 

63-8 

2-9 

82.0 

100.  2 

109-3 

18.5 

16 

9.14 

18.28 

27-42 

36.6 

45»7 

54-8 

64.0 

73-' 

82.3 

100.5 

109.7 

18.8 

17 

9-  '7 

18.34 

27-51 

36.7 

45-8 

55-o 

64.2 

73-4 

82.5 

100.9 

110.0 

19.2 

18 

9.20 

18-39 

27-59 

36.8 

46.0 

55-2 

64.4 

73-6 

82.8 

IOI.  I 

1  10.  4 

19.6 

»9 

9-23 

18-45 

i7.68 

36-9 

46.1 

55-3 

64.6 

73-8 

83.0 

101.5 

110.7 

19.9 

9.25 

I8.5I 

27-76 

37-0 

46.3 

55-5 

64.8 

74.0 

83-3 

ioi.  8 

III.O 

20.3 

91 

9.28 

18-57 

27-85 

37-1 

46.4 

55-7 

65.0 

74-3 

83-6 

102.  I 

ill.  4 

20.7 

22 

9-3' 

18.62 

27-94 

37-2 

46.6 

55-9 

65.2 

74-5 

83-8 

102.4 

111.7 

23 

9-34 

18.68 

28.02 

37-4 

46.7 

56.0 

65-4 

74-7 

84.1 

102.  7 

21.4 

24 

9-37 

18.74 

28.11 

37-5 

46.8 

56.2 

65-6 

75-0 

84-3 

103.  1 

112.4 

21.8 

25 

9.40 

18.80 

28.  19 

37-6 

47-0 

56.4 

65.8 

75-2 

84.6 

103-4 

112.8 

22.2 

26 

9-43 

18.85 

28.28 

37-7 

47-1 

56-5 

66.0 

75-4 

84.8 

103.7 

113.  1 

22-5 

27 

9/46 

18.  91 

28.37 

37-8 

47-3 

56-7 

66.2 

75-6 

85-1 

104.0 

"3-5 

22.9 

28 

9.48 

18.97 

28..  45 

37-9 

47-4 

56-9 

66.4 

75-9 

85-4 

104.3 

113-8 

23-3 

89 

9-51 

28.54 

38.0 

47.6 

57-  i 

66.6 

76.1 

85-6 

104.6 

114.1 

*3-7 

30 

9-54 

19.08 

28.62 

38-2 

47-7 

57-2 

66.8 

76.3 

85-9 

104.9 

1  14-  5 

24.0 

3' 

9-57 

19.14 

28.71 

38-3 

47-8 

57-4 

67.0 

76.6 

86.  I 

105-3 

114-8 

24-4 

32 

9.60 

19.20 

28.79 

38-4 

48.0 

57-6 

67.2 

76.8 

86.4 

105.6 

115-2 

24.8 

33 

9-63 

"9-25 

28.88 

38-5 

48.1 

57-8 

67.4 

77-0 

86.6 

105.9 

"5-  5 

25.  1 

34 

9.65 

'9-3' 

28.96 

38-6 

48-3 

57-9 

67.6 

77-2 

86.9 

106.2 

"5-9 

25-5 

35 

9.68 

J9-37 

29.05 

38-7 

48.4 

58-1 

67.8 

77-5 

87.2 

106.5 

116.2 

25-9 

36 

9-71 

19.42 

29-  >3 

38-8 

48.6 

58.3 

68.0 

77-7 

87-4 

106.8 

116.5 

26.2 

37 

9-74 

19.48 

29.  22 

39-0 

48.7 

58.5 

68.2 

77-9 

87.7 

107.  1 

116.9 

26.6 

38 

9-77 

"9-54 

29-3' 

39-  « 

48.9 

58-6 

68.4 

78.2 

87.9 

107-5 

117.2 

27.0 

39 

9.80 

19.60 

29-39 

39-2 

49-0 

58-8 

68.6 

78-4 

88.2 

107.8 

117.6 

27-4 

4» 

9-83 

•9-65 

29.48 

39-3 

49-2 

59-o 

68.8 

78.6 

88.5 

108.1 

118.  o 

27-7 

4< 

9.86 

19.71 

29.56 

39-4 

49-3 

59-2 

69.0 

78.8 

88.7 

108.4 

118.3 

28.1 

42 

9.  88 

'9-77 

29.65 

39-5 

49-4 

59-3 

69.2 

79-  i 

89.0 

108.  7 

1  1  8.  6 

28.5 

43 

9.91 

19.81 

29-73 

39-7 

49-6 

59-5 

69.4 

79-3 

89.2 

109.  o 

118.9 

28.8 

44 

9-94 

29.82 

39-8 

49-7 

59-6 

69.6 

79-5 

89-5 

109-3 

H9-3 

29.2 

45 

9-97 

19.94 

29.90 

39-9 

49-8 

59-8 

69.8 

79.8 

89-7 

109.7 

119.6 

29-6 

46 

O.  00 

19.99 

29.99 

40.0 

50.0 

60.  o 

70.0 

80.0 

90.0 

IIO.O 

120.0 

30.0 

47 

0.02 

20.  05 

30.08 

40.  i 

50.1 

60.2 

70.  2 

80.2 

90.2 

110.3 

120.3 

30-3 

48 

0.05 

20.  11 

30.16 

40.2 

50-3 

60.3 

70.4 

80.4 

9°-5 

1  10.  6 

120.6 

30-7 

49 

0.08 

20.  1  6 

30.25 

40.3 

50-4 

60.5 

70.6 

80.7 

90.8 

1  10.  9 

121.  0 

3«-' 

50 

0.  II 

20.22 

30.33 

40.4 

50.6 

60.7 

70.8 

80.9 

91.0 

III.  2 

121.3 

i'-4 

5' 
5a 

o.  14 

20.  28 

30.42 

40.6 

50.7 

60.8 

7  -o 

8  .1 

9«-3 

in.5 

I2I.7 

31-8 

53 

0.20 

20.  34 

20.  40 

3°-  5° 
30-59 

40.  7 
40.8 

50.  8 
51-0 

6  . 

7  -4 

8  .6 

91-  5 
91.8 

111-9 

112.  2 

122.4 

32.  2 

32.6 

54 
55 

0.  22 

20.45 

30.68 

0-9 

5  •« 

6  . 

7  -6 

8  .8 

92.0 

\\l:l 

122.7 

32-9 

56 

o.  25 

0.28 

20.  51 

20.57 

30.84 

f  J 

5  -4 

6  . 

72.0 

82.2 

92-  3 
92-  5 

113.  i 

123;  o 

123.4 

33-  3 

33.6 

57 

0.31 

20.63 

30-93 

I.  2 

5  -6 

6  . 

72.  2 

82,5 

92.8 

"3-4 

123.7 

58 

>0-  34 

20.68 

1.4 

5  -7 

62. 

72.4 

82.7 

93-0 

"3-7 

124.  1 

34-4 

59 

10.37 

62. 

72.6 

82.9 

93-3 

114.0 

124.4 

34-8 

Horz. 
Dist. 

99.08 

98.2 

297-2 

396.3 

495-4 

594 

694 

793 

892 

1090 

1-89  | 

1288 

Hor,  dist.  Is  for  30'  point.     Add  or  subtract  .055  ft.  to  each  100  ft.  of 
distance  for  each  19'  deoarture. 


TOPOGRAPHIC  STADIA  SURVEYING 


77 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 


1400 

1500 

1600 

1700 

1800 

1900 

2100 

2200 

2300 

2400 

2500 

2600 

/ 

21.6 
22.0 
22.4 
22.8 
23-2 

30.  2 

30.7 

31-  « 
31-5 
32.0 

138-9 
"39-4 
"39-8 
140.3 
140.  8 

147.6 
148.  i 
148.6 
149.  i 
149-5 

156.3 
156.8 
157-3 
•  57.8 
158.3 

65- 
65- 
66. 
66. 
67 

182.3 

182.9 
183-5 

184!  7 

191.0 
191.6 
192.3 
192.9 
193-5 

200.0 

200.  4 
201.  0 
201.  7 
202.  3 

208.  4 
209.  I 
209.7 
210.  5 

211.  I 

2  7-  i 

2  7.8 
2  8.5 
29-2 
2  9.9 

225-7 
226.5 
227.2 
228.0 
228.  7 

O 

2 

3 

4 

24.0 

24.4 
24.8 
25.2 

32.8 
33-2 

33-7 
34-  ' 

141.7 
142.1 
142.6 
143.0 

150.5 
151.0 
151-5 
152.0 

159-4 
159  9 
160.4 
1  60.  9 

68.2 

69^3 
69.9 

185-9 
186.5 

187^7 

194-8 
195-4 
196.0 
196.7 

203.  6 

204.3 
205.0 
205.6 

212.5 
"213.2 
213-9 
214.6 

2  1-4 
2  2.  I 
2  2.8 
23-5 

230.  2 
231.0 
23'-7 
232-4 

6 

8 
9 

26.0 

35-0 

144.0 

'53-o 

162.0 

7f.o 

188.9 

197.9 

206.9 

215.9 

2  4.  9 

233-9 

26.8 

35.8 

144.9 

153-9 

163.0 

72.  o 

190.  i 

199.  2 

208.  3 

217.3 

26.4 

235-4 

13 

27.6 

27.9 

28.4 
28.8 

36.7 
37-  ' 
& 

145.8 

146.  2 
M6.7 

154.9 

155.4 
155-9 

164.  o 

164.5 
165.0 

73-  I 

73-7 
74-  2 
74.8 

19I-4 

192.0 
192-5 
193-  l 

200.5 

201.  1 
202  3 

209.  6 
210.  2 

211.5 

218.7 
219-4 
220.  7 

2  78 
2  8.5 
2  9.9 

236.9 

237-7 
238.4 
239-1 

15 

16 
17 

29.S 
29.6 

30.0 
30.4 
30.8 

31-2 
3'.6 

32.0 
32-4 
32-8 
33-2 
33-6 

34-0 

38.4 
38.8 

39-3 
39-7 
40.  i 
40-5 
41.0 

41.4 
41.9 
42.3 
42-7 
43-  > 

43-6 

147.  6 
148.1 

148.5 
149.0 
149.4 
"59  9 
150.4 

I50-9 
I5I-3 
l5>-7 
152-2 
152-6 

'53-1 

156-8 
157-3 

.57.8 
158-3 
158.8 
•59-3 
159-8 

160.2 
1  60.  7 
161.2 
161.7 
162.  3 

162.7 

1  66.  I 
166.6 

167.  1 
167.  6 
168.  i 
168.6 
169.2 

169-7 
170.2 
170.7 

171.  2 

171  7 
172.2 

75-3 
75-8 

76.4 
76.9 
77-5 
78.0 
78.6 

79  I 
79  7 
So.  2 
80.7 
81.3 

81.8 

193.7 
194.3 

195-0 
'95  6 
196.2 
196.7 
197.3 

197.9 
198.6 
199-2 
199-7 
200.'  3 

200.  9 

204.2 
204.9 

205.  5 
206.  i 
206.7 

207.4 
268.0 
208.6 
209.3 
209.9 

210.  5 

213.5 
214.2 

214.  8 

215.5 

216.  I 

216.8 
217.5 

218.  i 

218.8 
219.4 

220.  I 

222.  8 
223-5 
224.2 
224.9 
225-5 

226.2 

226.  9 
227.6 
228.  3 
229.0 

229.7 

232.1 

232.8 
233-5 
234-2 
234-9 

235.6 
236.4 
237-1 
237-8 
238-5 

239-2 

239  9 

241.4 
242.  i 
242.9 
243-6 
244-3 

245.1 
245-8 
246.6 
247-3 
248.  o 

248.8 

19 
20 

21 

22 
23 
24 
25 

26 
27 
28 
29 
30 

3» 

34-8 
35-2 

44-4 
44-8 

154-0 
154-5 

163.6 
164.1 

173.8 

83  4 

202.7 

212.4 

222.  1 

231  7 

241.4 

251.0 

33 
34 

36.0 
36.4 
36.8 

45-7 
46.1 
46.5 

155-4 
155-8 
156-3 
156  8 

165.1 
165.6 
166.  i 

174-8 
175-3 
175  8 

84-5 
85.1 
85  6 

203-9 

204.  5 
205.  i 

2  3-7 
2  4-3 

2  4.9 

223.4 

224.  o 

224.7 

233-  i 
233-8 
234-5 

242.  8 
243-5 

244.  2 

252  5 
253-3 

254  .0 

36 
1 

37-6 
38.0 

47-4 
47-8 

157-2 
157.7 

167.  o 
167.  5 

176.9 
177-4 

86.7 
87.2 

206.  3 
206.9 

2  6.  2 

2  6.  8 

226.0 
226.  7 

235-8 
•236.  5 

245-6 
246-4 

255-5 

256.  2 

40 
41 

38.8 
39  2 

48.7 
49-  1 

158-6 
"59-0 

168.5 
169.0 

178.4 
178  9 

88.3 
89.9 

208.  i 
208.7 

280 

2  8.7 

227.9 
228.6 

237  9 
238.6 

247.8 
248.5 

257-7 
258.4 

43 

44 

40.  4 
40.8 

50.0 
5°-4 
50.8 

160.0 
160.4 
160.9 

169.9 
170.  4 
170.9 

179-9 

.80.5 

89.9 
90.  5 

209.  9 
210.  5 

299 

229.9 
230.  6 

239-9 
240.  6 

249.9 
250.  6 

259-9 

260.  7 
261.4 

46 
47 
48 

4  .6 

,61.8 

263.6 

50 
51 

4  -4 
4  -8 

52.5 
52-9 

162.  7 
163.1 

173-3 

183-5 

93-7 

2  4-  i 

224-3 

234-5 

244-7 

254-2 
254.9 

264.4 
265.1 

52 

53 

43-6 

53-8 

164.1 

174-3 

184.6 

94.8 

2  5-3 

225-6 

235.8 

246.1 

256.3 

266.6 

55 

44-3 
44.8 
45-1 

54-6 
55-  ' 

55-5 

165.  o 
165-4 
165.  9 

175.3 
175-8 
176.2 

185.6 
186.1 
186.6 

95-9 
96.4 

2  6.5 
2  7.  1 

226.  8 
227.4 

UK 

247.4 
248.1 

2578 
258-5 

268.  i 
268.8 
269.5 

12 

59 

1387 

1486 

1585 

1684 

1783 

1882 

2081 

Horz. 
Dist. 

Hot.  dist.  is  for  30'  point.     Add  or  subtract  .055  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


78 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
6° 


f 

too 

200 

3QO 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

0.40 

20.79 

3'-  19 

41.6 

52.0 

62.4 

72.8 

83.2 

93-6 

114.4 

124.7 

135-  1 

0.42 

20.  85 

3I-27 

41-7 

S2-  i 

62.5 

73-o 

83.4 

93-8 

14-7 

25-  i 

135-5 

0-45 

20.90 

3'-  36 

41.8 

52-3 

62.7 

73-2 

83.6 

94-1 

15-0 

25-4 

135-9 

o.  48 

20.96 

3<-44 

41.9 

52-4 

62.9 

73-4 

83.8 

94-3 

'5-3 

25-8 

136-2 

0.51 

21.02 

31-53 

42.0 

52-5 

63-1 

73-6 

84.1 

94-6 

15-6 

26.1 

•  36.6 

0-54 

21.  08 

31-6. 

42.2 

52-7 

63.2 

73-8 

84-3 

94-8 

15-9 

26.5 

137-0 

o.57 

21.13 

31-69 

42.3 

52.8 

63-4 

74.0 

84.5 

95-  i 

16.  2 

26.8 

137-4 

o.59 

•19 

3L78 

42-4 

53-o 

63.6 

74-2 

84.8 

95-4 

'6.5 

27.1 

137-7 

o.  62 

.25 

3'-  87 

42-5 

53-1 

63.7 

74-4 

85.0 

95-6 

16.  8 

27-5 

138-1 

0.65 

•30 

31-95 

42.6 

53-3 

63-9 

74-6 

85-2 

95-9 

17.2 

27.8 

138.5 

1 

0.68 

.36 

32-04 

42.  7 

53-4 

64.1 

74-8 

85-4 

96.1 

17-5 

28.2 

138-8 

II 

6.71 

•42 

32.12 

42.8 

53-5 
53-  7 

64.3 
64.  4 

75-o 

85.7 
85.  9 

96.4 

96  6 

17.8 
18   I 

28.5 
28.  8 

139-2 
•  39-  6 

13 

o.  76 

•53 

32-30 

43-  i 

53-8 

64^6 

75-4 

86.  i 

yu.  v 
96.9 

,8.4 

29.  2 

139-9 

14 

0.79 

•59 

32.38 

43-2 

54-0 

64.8 

75-6 

86.3 

97-  > 

18.7 

29  5 

140-3 

15 

0.82 

•  64 

32.47 

43-3 

54-1 

64.9 

75-8 

86.6 

97-4 

19.0 

29-9 

140.7 

16 

0.85 

.70 

32.55 

43-4 

54-2 

65.1 

76.  o 

86.8 

97.6 

19.4 

30.2 

141.1 

17 

0.88 

-76 

32-64 

43-5 

54-4 

65-3 

76.2 

87.0 

97-9 

'9-7 

30.5 

141.4 

18 

o.  91 

.81 

32.72 

43-6 

54-5 

65.4 

76.3 

87-3 

98.2 

20.0 

30-9 

141.8 

19 

0.94 

-87 

32-8, 

43-7 

54-7 

76.5 

87.5 

98.4 

20.3 

3'-  2 

142.2 

20 

0.96 

•93 

32-89 

43-9 

54-8 

65.8 

76.7 

87-7 

98.7 

20.6 

31.6 

142-5 

21 

0-99" 

.98 

32.98 

44-0 

55-0 

66.0 

76.9 

87.9 

98.9 

20.9 

31.9 

142.9 

22 

•  04 

33-06 

44.  i 

55-  1 

66.1 

77-1 

88.2 

99-2 

21.  2 

32.2 

143-3 

23 

1.05 

.  10 

33-15 

44.2 

55-2 

66.3 

77-3 

88.4 

99-4 

21-5 

32.6 

M3-6 

24 

i.  off 

.  16 

33-23 

44-3 

55-4 

66.5 
66.  6 

77-5 

88.6 
88.8 

99-7 

21.8 

32.9 

144.0 

26 

11.13 

•27 

33-40 

44-5 

55-  5 
55-7 

66.8 

77-9 

89.1 

OO.  2 

22.5 

33.6 

144-7 

27 

•  33 

33-49 

44-6 

55-8 

67.0 

78.1 

89-3 

00.5 

22.8 

34-0 

I4S-I 

28 

it.  19 

•38 

33-57 

44.8 

56.0 

67.1 

78.3 

89-5 

00.7 

23-1 

34-3 

H5-5 

29 

II.  22 

•44 

33-66 

44-9 

56.1 
c6  2 

67-3 

67   c 

78-5 
78.  7 

89.7 

01.  0 

23-4 

34-6 

,45.8 

3° 
31 

1  1.  25 
11.28 

•  49 
•55 

33.83 

45-1 

50.  Z 

56.4 

07.  5 

67.7 

78.9 

90.2 

01.5 

24.0 

35-3 

146.6 

32 

11.30 

.61 

33-91 

45-2 

56-5 

67.8 

79-  » 

90.4 

01.7 

24-3 

35-6 

147.0 

33 

11.32 

.66 

34-oo 

45-3 

56.7 

68.0 

79-3 

90.7 

02.0 

24.7 

36.0 

M7-  3 

34 

11.36 

.72 

34.08 

45-4 

56.8 

68.2 

79-5 

90.9 

O2.  2 

25-0 

36.3 

147-7 

35 

"•39 

.78 

34-17 

45-6 

56-9 

68.3 

79-7 

91.  i 

02-5 

25-3 

36.7 

148.1 

36 

11.42 

.84 

34-25 

45-7 

57-  I 

68.  5 

79-9 

91-3 

02.8 

25.6 

37-0 

148.4 

37 

11-45 

•89 

34-34 

45-8 

57-2 

68.7 

80.  i 

91.6 

03.0 

25-9 

37-4 

148.8 

38 

1  1  -.47 

•95 

34-42 

45-9 

57-4 

68.8 

80.3 

91.8 

03-3 

26.2 

37-7 

149-2 

39 

11-50 

.00 

34-51 

46.0 

57-5 

69.0 

80.5 

92.0 

03.5 

26.5 

38.0 

149-5 

40 

.06 

34-59 

46.1 

57-6 

69.2 

80.7 

92.2 

03-8 

26.8 

38-4 

149-9 

41 

11-56 

.  12 

34-68 

46.2 

57-8 

69.4 

80.9 

92-5 

04-0 

27.1 

38.7 

I50.3 

42 

11-59 

.  18 

34-76 

46-4 

57-9 

69-5 

81. 

92.7 

04-3 

27-5 

39-0 

150-6 

43 

11.62 

•23 

34-84 

46-5 

58.. 

69-7 

81. 

92.9 

04-5 

27.8 

39-4 

I       .0 

44 

11.64 

.29 

34-93 

46.6 

58.2 

69.9 

81. 

93-2 

04.8 

28.  i 

39-7 

i     •  4 

45 

11.67 

3-34 

35-02 

46.7 

58-4 

70.0 

81. 

93-4 

05.0 

28.4 

40.1 

I     -7 

46 

11.70 

3-40 

35-10 

46.8 

58.5 

70- 

81. 

93-6 

05-3 

28.7 

40.4 

I      .  L 

47 

it-73 

3.46 

35-19 

46.9 

58.6 

70. 

82. 

93-8 

05.6 

29.0 

40.7 

I     -5 

40 

11.76 

3-5" 

35-27 

47-0 

58.8 

70. 

82. 

94-1 

05.8 

29-3 

I.  I 

i     .8 

49 

II-79 

3-57 

35-36 

47-  I 

58-9 

70. 

82. 

94-3 

06.  I 

29.6 

1-4 

153-2 

50 

1  1.  8.1 

3-63 

35-44 

47-3 

59-1 

70. 

82. 

94-5 

06.3 

29-9 

1.8 

1536 

51 

11.84 

3-68 

35-53 

47-4 

59-2 

82. 

94-7 

06.6 

30.3 

2.  I 

153-9 

52 

11.87 

3-74 

35-6i 

47-5 

59-4 

83- 

95-o 

06.8 

30.6 

2-4 

154-3 

53 

11.90 

3.8o 

35-70 

47-6 

59-5 

83-3 

95-2 

07-1 

30-9 

42.8 

«54.7 

54 

"•93 

3-85 

35.78 

47-7 

59-6 

83.5 

95-4 

07-3 

3'- 

43-  ' 

155-0 

55 

11.96 

3-91 

35-86 

47-8 

59-8 

83-7 

95-6 

07-6 

3'- 

43-5 

'55-4 

56- 

11.98 

3-97 

35-95 

47-9 

59-9 

7'. 

83-9 

95-9 

07.8 

31- 

43-8 

155-8 

57 

12.01 

4.02 

36-03 

48.0 

60.  i 

72. 

84.1 

96.1 

08.  I 

32- 

44-1 

156-1 

58 
59 

12.04 

12.07 

24.08 
24-  "4 

36.  20 

48.2 
48-3 

60.2 
60.3 

72. 
72. 

84.3 
84-5 

96-3 
96.5 

08.4 
08.7 

32- 
32- 

44-5 
44-8 

156.5 
156.9 

Horz. 
Dist. 

98.72 

'97-4 

296.2 

394-9 

493-6 

592 

691 

790 

888 

1086 

1185 

1283 

Hor.  dist.  Is  for  30'  point.     Add  or  subtract  .065  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


79 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 

7° 


100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1200 

1300 

r 

2.  10 

24.  19 

36.29 

48.4 

60.5 

72.6 

84.7 

96.8 

08.  9 

<33-' 

145-2 

157-2 

1.  12 

24-25 

36.37 

48-5 

60.6 

72.7 

84.9 

97-o 

09.  i 

133.4 

145-5 

157-6 

'•  IS 

24-30 

36.46 

48.6 

60.8 

72.9 

85.1 

97-2 

09.4 

133-7 

•45-8 

158.0 

2.18 

24.  36 

36-54 

48.7 

60.9 

73-1 

85-3 

97-4 

09.  6 

134-0 

146.  2 

158.4 

2.  21 

24.42 

36-63 

48.8 

61.  I 

73-2 

85-5 

-97-7 

09.  9 

>34-3 

M6.5 

158.7 

2.24 

24-47 

36.71 

48.9 

61.2 

73-4 

85.7 

W-9 

10.  I 

134-6 

146.8 

I59-I 

12.27 

24-53 

36.80 

49.1 

61.3 

73-6 

85.9 

98.1 

10.4 

134-9 

147-2 

159.4 

12.29 

24-59 

36.88 

49-2 

61.5 

73-8 

86.0 

98.3 

10.  6 

135-2 

147-5 

159.8 

12.32 

24-64 

36.97 

49-3 

61.6 

73-9 

86.2 

98.  6 

10.  9 

135-5 

147-9 

I&0..2 

"2-35 

24.70 

37-  05 

49-4 

61.8 

74-  i 

86.4 

98.8 

II.  2 

135.8 

I48.2 

I60.6 

.2.38 

24-76 

37-  i  J 

49-5 

61.  9 

74-3 

86.6 

99-o 

II.4 

136.2 

148.6 

160.9 

i 

12.41 

24.81 

37-  22 

49.6 

62.0 

74-4 

86.8 

99.2 

n-7 

136.5 

148.9 

I6I.3 

,, 

12-43 

24.87 

37-30 

49-7 

2.  2 

74-6 

87.0 

99-5 

11.9 

136.8 

149.2 

161.6 

1  2 

12.46 

24.  92 

37-39 

49-8 

2-3 

74-8 

87-2 

99-7 

12.  2 

'37-  i 

149.6 

162.0 

13 

12.49 

24.98 

37-47 

50.0 

2-5 

74-9 

87-4 

99-9 

12.4 

137-4 

149.  9 

162.4 

M 

12.52 

25  04 

37-56 

50.  I 

2.6 

75-' 

87.6 

100.  2 

12.7 

'37-7 

150.2 

162.7 

15 

iz-55 

25-09 

37.64 

50.2 

2.7 

75-3 

87.8 

00.4 

12.9 

138.0 

150.  6 

163.1 

16 

•  2-58 

25-  15 

37-73 

50.3 

2-9 

75-4 

oo.  6 

'3-2 

138.3 
i  ifi   A 

'50-9 

163-5 
163.  8 

17 
18 

12-63 

25.26 

37.89 

50-5 

63.2 

75-8 

88.4 

01.  0 

'3-  4 
'3-7 

130.  o 

138.9 

151.  2 
151.6 

164.2 

•9 

12.66 

25-32 

37.98 

50.6 

63.3 

76.0 

88^6 

01.3 

13-9 

'39-3 

15'.9 

164.6 

20 

12.69 

25-38 

38.06 

50.8 

63.4 

76.1 

88.8 

01.5 

14.2 

139-6 

152.3 

164.9 

21 

12.72 

25-43 

38.15 

50.9 

63.6 

76.3 

89.0 

01.7 

14.4 

139-9 

152.6 

165-3 

22 

2-74 

25-49 

38.23 

S'.o 

63.7 

76-5 

89.2 

02.  0 

•4-7 

140.2 

I52.9 

165-7 

23 

12.77 

25-54 

38-32 

51-1 

63.9 

76.6 

89.4 

1O2.  2 

15.0 

140.5 

153-3 

166.0 

24 

12.80 

25.60 

38.40 

5'-2 

64.0 

76.8 

89.6 

102.4 

"5-2 

140.8 

'53-6 

166.4 

25 

12.83 

25-66 

38.49 

Si-3 

64.1 

77-0 

90.0 

IO2.  6 

"5-5 

14  .1 

153-9 

166.8 

26 

12.86 

25-71 

38.57 

5'-4 

64.3 

77-  I 

90.0 

102.  8 

15-7 

14  .4 

154-3 

167.1 

27 

12.88 

25-77 

38.65 

51-5 

64.4 

77-3 

90.2 

103.  I 

14  •  7 

•54.6 

167.4 

12.  91 

12.  94 

25.  83 
25.88 

38.  74 
38.82 

51.8 

64.7 

77-6 

90.6 

103.5 

16.5 

14  .4 

155-3 

168.2 

30 

12.97 

25-94 

38-91 

51-9 

64.8 

77.8 

90.8 

103.8 

16.7 

«42.7 

155-6 

168.6 

31 

13-00 

25-99 

38.99 

52.  o 

65.0 

78.0 

91.0 

104.0 

17.0 

143.0 

156.0 

169.0 

32 

13.  02 

26.05 
26.  ii 

39.08 

52.  i 

52.  2 

65.1 

65  3 

78.1 

91.2 

04.2 

17.2 

143-3 

156.3 
156.  6 

169.3 
169.  7 

33 

I3-08 

26.  16 

39-24 

52-3 

65.4 

72-5 

91.6 

04.6 

'7-7 

143-9 

157-0 

170.0 

35 

13    'I 

26.22 

39-33 

52.4 

65.5 

ra-  7 

91.8 

104.9 

18.0 

144.2 

>57-3 

170.4 

36 

13-  '4 

26.28 

39-41 

52-6 

65.7 

78.8 

92.0 

105.1 

18.  2 

144-5 

157-6 

170.8 

37 

13-  '7 

26.33 

39-50 

52.7 

65.8 

79.0 

92.2 

105.3 

18.5 

M4.8 

•  58.0 

171.2 

38 

13-20 

26.40 

39.60 

52-8 

66.0 

79.2 

92.4 

105.6 

18.8 

145-2 

158.  4 

171.6 

39 

13-22 

26.44 

39-66 

52.9 

66.1 

79-3 

92.6 

105.8 

19.  o 

145.4 

158.7 

17.1.9 

40 

•3-25 
13-28 

26.  50 
26.56 

39-75 
39-83 

53-o 
53-  t 

66.2 
66.4 

79-5 
79-7 

92.8 
92-9 

106.  o 
106.2 

19.2 
19-5 

a: 

"59-0 
159.3 

172.2 
172.6 

41 
4» 

13-3" 

26.61 

39-92 

53-2 

66.5 

79-8 

93-  i 

106.4 

19.8 

146.4 

159-7 

173-0 

43 

'3-33 

26.67 

40.00 

53-3 

66.7 

80.0 

93-3 

106.7 

20.0 

146.7 

160.  o 

173-3 

44 

'3-36 

26.  72 

40.09 

53-4 

66.8 

80.2 

93-5 

106.9 

20.3 

147.0 

t6o.3 

173-7 

45 

'3-39 

26.78 

40.17 

53-6 

67-0 

8o.7 

93-7 

107.1 

20.  5 

147'.  2 

160.6 

174.0 

46 

!3*  42 
'3-45 

26^9 

40.  25 
40-34 

53-  7 

53.8 

67.    I 

67.2 

80.  5 

80.7 

93-9 

94-  ' 

i°7-  3 
107.  6 

21.0 

147-9 

161.4 

174.  4 
174.8 

47 

48 

'3-47 

26.94 

40.42 

53-9 

67-4 

80.8 

94-3 

107.8 

21-3 

148.2 

161.7 

175-2 

49 

13-50 

27.00 

40.50 

54-0 

67.5 

81.0 

94-5 

108.0 

21.5 

148.6 

162.0 

«75-5 

50 

13-53 

^7-o6 

40.59 

54-' 

67.7 

8    .2 

94-7 

108.2 

21.8 

148.8 

162.4 

"75-9 

51 

13.56 

27.  12 

40-67 

54-2 

67.8 

8  -3 

94-9 

108.5 

22.  O 

149.1 

162.7 

176,2 

52 

«3-59 

27.17 

40.76 

54-3 

67.9 

8  .5 

95-  « 

108.7 

22.3 

149.4 

163.0 

176.6 

53 

13-61 

27.23 

40.84 

54-  5 

68.  I 

8  .7 

95-3 

108.9 

22.5 

149-8 

'63.4 

177.0 

54 

13-64 

27-28 

40.93 

54-6 

68.2 

8  .8 

95-5 

109.1 

22.8 

I50.I 

'63-7 

'77-3 

55 

13-67 

27-34 

41.  01 

54-7 

68.4 

82.0 

95-7 

109.4 

23.0 

'50-4 

164.0 

177-7 

5* 

13-70 

27.40 

41.09 

54-8 

68.5 

82.2 

95-9 

109.6 

23-3 

150.7 

164-4 

•  78.1 

57 

'3-73 
13-75 

27-45 
27.5I 

41.18 
41.26 

54-9 
55-0 

68.6 
68.8 

82.4 
82.5 

96.1 
96.3 

109-8 
tio.  o 

23.5 
23-8 

151-0 
«5i-3 

164.7 
165.0 

178.4 
178.8 

58 
59 

98.29 

196.6 

294.9 

393-2 

491.4 

590 

688 

786 

885 

1081 

1179 

1278 

Horz. 
Dist. 

Hor.  dist.  is  for  30'  ppint.     Add  or  subtract  .075  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


80 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
8° 


/ 

100 

200 

300 

400 

500 

600 

700 

800 

000 

1100 

t 

o 

13.78 

27-56 

4«-35 

55-  ' 

68.9 

82.7 

96.5 

10.3 

124.0 

151.6 

O 

I 

13-81 

27.62 

41-43 

55-2 

69.0 

82.9 

96-7 

10.5 

124.3 

151-9 

2 

13-84 

27.68 

4i-5i. 

55-4 

69.2 

83.0 

96.9 

10.7 

124-  5 

152.  2 

2 

3 

13-87 

27-73 

41.  60 

55-5 

69-3 

83-2 

97-i 

10.  9 

124.8 

152.  5 

3 

4 

13-89 

27.78 

41-68 

55-6 

69-5 

83-4 

97-3 

II.  2 

125.0 

152.8 

4 

5 

13.92 

27-84 

41-76 

55-7 

69.6 

83-5 

97-4 

II-  4 

125-3 

153-  i 

5 

6 

13-95 

27.90 

41-85 

55-8 

69.8 

83-7 

97.6 

ii.  6 

125.6 

153-4 

6. 

7 

13-98- 

27-96 

41-93 

55-9 

69-9 

83-9 

97-8 

n.  8 

125.8 

153-8 

7 

8_ 

14.01 

28.01 

42.02 

56.0 

70.0 

84.0 

98.0 

12.0 

126.0 

154-1 

8 

9 

'4-03 

28.07 

42.10 

56.1 

70.2 

84.2 

98.2 

12.3 

126.3 

154-  4 

9 

to 

14.06 

28.12 

42.18 

56.2 

70.3 

84.4 

98.4 

12-5 

126.6 

154-7 

Ii 

14.09 

28.18 

42.27 

56.4 

cA  e 

70.4 

?r>  ft 

84-5 

98.6 

08  8 

12.7 

126.8 

155-0 

ii 

13 

14.  14 

28.29 

42-44 

5°-  5 

56.6 

70.  o 
70.7 

84.  7 

84-9 

90.  8 

99-o 

12.  9 

13-2 

127.3 

155-  3 
155-6 

13 

14 

14-17 

28.35 

42-52 

56.7 

70.9 

85.0 

99.2 

13.4 

,27.6 

155-9 

14 

«5 

14.  20 

28.40 

42.  60 

56.8 

71.0 

85.2 

99-4 

13.6 

127.8 

156-2 

15 

16- 

14-23 

28.46 

42.68 

56.9 

.  I 

85-4 

99-6 

13.8 

128.0 

156.5 

6 

17 

14.26 

28.51 

42.77 

57-0 

•  3 

85-5 

99.8 

14.0 

128.3 

156.8 

7 

18 

14.28 

28.57 

42.85 

57-  1 

.  4 

85-7 

14.3 

128.6 

157-1 

8 

>9 

14-  3« 

28.62 

42.94 

57-2 

.6 

85-9 

00.  2 

14-5 

128.8 

157-4 

9 

20 

14-34 

28.68 

43-02 

57-4 

•7 

86.0 

00.4 

«4-7 

129.1 

157-7 

o 

21 

M-37 

28.74 

43-  10 

57-5 

71-8 

86.2 

oo.  6 

14.9 

129.3 

158.0 

i 

22 

14.40 

28.79 

43-  '9 

57-6 

72.0 

86.4 

oo.  8 

IS-  * 

,29.6 

.58.4 

2 

23 

14.42 

28.95 

43-27 

57-7 

72.1 

86.5 

01.  0 

15-4 

129-8 

158.7 

3 

24 

"4-45 

28.90 

43-36 

57-8 

72-3 

86.7 

OI.  2 

15-6 

130.1 

159.0 

24 

*5 

14-48 

29.96 

43-44 

57-9 

72-4 

86.9 

01.4 

5-8 

I30-3 

159-3 

25 

26 

'4-5' 

29.02 

43-52 

58.0 

72.5 

87,0 

o  .6 

16.  i 

130.6 

159-6 

26 

27 

14-54 

29.07 

43-  60 

58-1 

72-7 

87.2 

o  -7 

6-3 

130.8 

159-9 

27 

28 

14-56 

29-  13 

43-69 

58.2 

72.8 

87.4 

o  .9 

16.5 

131-1 

160.2 

28 

29 

14-59 

29.18 

43-77 

58-4 

73-o 

87.6 

16.7 

131-3 

160.5 

29 

3° 

14.62 

29.24 

43-85 

58.5 

73-  i 

87.7 

o  .3 

16.9 

131-6 

160.8 

30 

31 

.4-65 

29.29 

43-94 

58.6 

73-2 

87.9 

o  .  5 

17.2 

131-8 

16  .1 

31 

32 

14-67 

29-35 

44.02 

58.7 

73-4 

88.0 

o  -7 

17-4 

132-  i 

16  .4 

32 

33 

14.70 

29.40 

44-  " 

58.8 

73-5 

88.2 

o  .9 

17.6 

132-3 

16  .7 

33 

34 
35 

!t* 

29.  46 
29-52 

44-  '9 
44-27 

58.  9 
59-o 

73-  6 
73-8 

88.6 

o  -3 

18.  i 

132.  8 

16  .3 

34 
35 

36 

14-79 

29-57 

44-36 

59-1 

73-9 

88.7 

03.5 

18.3 

133-1 

16  .6 

36 

37 

i4.8i 

29-63 

44-44 

59-2 

74-  I 

88.9 

03.7 

18.5 

133-3 

16  .9 

37 

38 

14.84 

29.68 

44-52 

59-4 

74-2 

89.0 

03.9 

18.7 

133-6 

163.2 

38 

39 

14.87 

29-74 

44.61 

59-5 

74-3 

89.2 

04.  1 

19.0 

'33-8 

163.6 

39 

4<> 

14.90 

29.78 

44.69 

59-6 

74-5 

89.4 

04.3 

19.2 

'34-  « 

163-9 

40 

41 

14.92 

29-85 

44-77 

59-7 

74-6 

89.6 

04.5 

19-4 

134-3 

164.2 

41 

42 

14-95 

29.90 

44.86 

59-8 

74-8 

89.7 

04.7 

19.6 

134-6 

164-5 

42 

43 

14.98 

29.96 

44-94 

59-9 

74-9 

89.9 

04.9 

19.8 

134-8 

164.8 

43 

44 

15.01 

30.  02 

45-02 

60.0 

75-o 

90.0 

05.0 

135-1 

165.1 

44 

45 

»5-°4 

30-07 

45-  li 

60.  i 

75-2 

90.2 

05.2 

20.3 

135-3 

165-4 

45 

46 

15.06 

30-13 

45-18 

60.2 

75-3 

90.4 

05.4 

20.5 

•35-6 

165.7 

46 

47 

'5-09 

30.  1  8 

45-27 

60.4 

75-5 

90.6 

05.6 

20.7 

135-8 

166.0 

47 

48 

15-12 

30-24 

45-36 

60.5 

75-6 

90.7 

05.8 

21.0 

136-1 

166.3 

48 

49 

IS-  '5 

30-29 

45-44 

60.6 

75-7 

90.9 

06.  o 

2  .  2 

136.3 

166.6 

49 

5° 

15-  «7 

30-35 

45-52 

60.7 

75-9 

9  .0 

06.2 

2  -4 

136.6 

166.9 

y> 

-5« 

15-20 

30.40 

45-  60 

60.8 

76.0 

06.4 

2  .6 

136.8 

167.2 

51 

52 

«5-23 

30-46 

45-69 

6o.-9 

76.2 

06.6 

2  .8 

I37-I 

<6?-5 

52 

53 
54 

15.  26 
15-28 

30.51 
30.57 

45-77 
45-86 

.0 

.  i 

76-3 
76.4 

. 

06.8 
07.0 

2  .  I 
2  -3 

137-3 
137-6 

167.8 
168.1 

53 

54 

55 

«5-3« 

30.  62 

45-94 

.  2 

76.6 

07.2 

2  -5 

•37-8 

168.4 

55 

56 

15-34 

30.68 

46.02 

•  4 

76.7 

07.4 

122.7 

138.1 

168.7 

56 

57 

15-37 

30.74 

46.  10 

•  J 

76.8 

07.6 

122-9 

138.3 

169.0 

57 

58 

15-40 

30.79 

46.19 

.6 

77-o 

07.8 

123.2 

.38-6 

169-4 

58 

59 

15-42 

30.85 

46.  27 

•7 

77-  i 

08.0 

123-4 

138.8 

169.  6 

59 

Horz. 
Dist. 

97.82 

195-6 

293;  5 

391-3 

489.  I 

587 

685 

783 

880 

1076 

Horz. 
Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .085  ft.  to  each   ipo  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


81 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
9° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

f 

15-45 

30.90 

46.35 

.8 

77-3 

92.7 

08.2 

123.6 

139.  i 

170.0 

O 

15-48 

30.96 

46.44 

•  9 

77-4 

92.9 

08.4 

.23.8 

•39-3 

170.  3 

I5-5I 

31-01 

46.52 

.  o 

77-5 

93-o 

08.5 

124.0 

139-6 

170.6 

2 

15-53 

31-07 

46.60 

.  i 

77-7 

93-2 

08.7 

124.3 

139-8 

170.  9 

^ 

15-56 

31.12 

46.68 

.  2 

77-8 

93-4 

108.9 

124-5 

140.0 

171.2 

4 

15-59 

31-18 

46.77 

•4 

77-9 

93-5 

09.  i 

124.7 

140.3 

171-5 

5 

15-62 

31-23 

46.85 

2-5 

78.1 

93-7 

09-3 

124.9 

140.6 

171.8 

6 

15-64 

31-29 

46.93 

2.6 

78.2 

93-9 

09-5 

125.  2 

140.8 

172.  i 

7 

15-67 

3'-34 

47-02 

2-7 

78.4 

09-7 

125.4 

141.0 

172-4 

8 

15-70 

47-  10 

2.8 

78.5 

94  2 

09-9 

125.6 

141-3 

172.7 

9 

10 

15-73 

31-45 

47-18 

62.9 

78.6 

94-4 

10.  I 

125.8 

141-5 

173-0 

10 

II 

15-76 

3i  5' 

47.26 

63.0 

78.8 

94-5 

0.3 

126.0 

141.8 

173-3 

ir 

12 

15-78 

31-'  56 

47-35 

63.1 

78.9 

94-7 

o.  5 

126.3 

142.0 

173-6 

12 

13 

15-8. 

31.62 

47-43 

63.2 

79.0 

"94-9 

0.7 

126.5 

142.3 

173-  9 

13 

M 

15-84 

31.68 

47-51 

63.4 

79-2 

95-o 

a  9 

126-7 

174-  2 

!4 

15 

15.86 

3'-73 

47.60 

63.5 

79-3 

95-2 

i.  i- 

126-9 

142*8 

174.5 

IS 

16 

15-89 

31-79 

47.68 

63.6 

79-5 

95-4 

.  2 

127.  I 

143-0 

174-  8 

16 

•7 

15-92 

47-76 

63.7 

79-6 

95-5 

.  4 

•27.4 

143-3 

•75-  i 

17 

18 

15-95 

31-90 

47-  84 

63.8 

79-7 

95-7 

.6 

127.  6 

143-5 

175-4 

18 

19    i 

15.98 

31-95 

47-93 

63.9 

79-9 

95-8 

8 

127.8 

143-8 

•75-  7 

19 

20 

16.00 

32.01 

48.01 

64.0 

80.0 

96.0 

.O 

128.0 

144.0 

176.0 

20 

21 

16.03 

32.06 

48-09 

64.1 

80.2 

96.2 

.2 

128.2 

144-3 

176.3 

21 

22 

16.06 

32.12 

48.17 

64.2 

80.3 

96-4 

•  4 

128.5 

144-5 

176.6 

22 

23 

16.09 

32-17 

48.26 

64-3 

80.4 

96-5 

.6 

128.7 

144.8 

176.9 

23 

24 

16.  n 

32-23 

48.34 

64.4 

80.6 

96.7 

.8 

128.9 

•45-0 

177.  2 

24 

25 

16.14 

32.28 

48.42 

64.6 

80.7 

96.8 

3-0 

129.1 

145-3 

177.6 

25 

26 

16.17 

32.34 

48.51 

64.7 

80.8 

97-  o 

3-2 

129.4 

145-5 

177.8 

26 

27 

1  6.  20 

32-39 

48.59 

64.8 

81.  o 

97-2 

3-4 

129.6 

145-8 

178.2 

27 

28 

16.  22 

32.45 

48.67 

64.9 

81.1 

97-3 

3-6 

146.0 

•78.5 

28 

29 

•  6.25 

32-50 

48.75 

65.0 

81.3 

97-5 

8 

130.0 

146.3 

I78.8 

29 

3° 

16.28 

32.56 

48.84 

65.1 

81.4 

97-7 

0 

130.2 

I79.I 

30 

31 

16.31 

32.61 

48.92 

65.2 

81.5 

97-8 

, 

130.4 

146.8 

179  4 

31 

32 

16.33 

32-67 

49.00 

65.3 

81.  7 

98.0 

3 

130.7 

147.0 

179-7 

3* 

33 

•  6.36 

32.72 

49.08 

65.4 

81.8 

98.2 

5 

130.9 

147.2 

180.0 

33 

34 

i6.39 

32.78 

49-17 

65.6 

81.9 

98-3 

7 

131.  i 

147-5 

180.3 

34 

35 

16.42 

32-83 

49-25 

65.7 

82.1 

98.5 

9 

147.7 

180.6 

35 

36 

16.44 

32-89 

49-33 

65.8 

82.2 

98.7 

5-  i 

131-6 

148.0 

180.9 

36 

37 

16.47 

32-94 

49-41 

65.9 

82.4 

5-3 

i3'-8 

148.2 

181.2 

37 

38 

1  6.  50 

33-oo 

49-  50 

66.0 

82.5 

99-0 

5-5 

132.0 

148.5 

181.5 

3» 

39 

16-53 

33-05 

49-  58 

66.1 

•82.6 

99.2 

5-7 

132-2 

148.7 

181.8 

39 

40 

i-  55 

33-11 

49.66 

66.2 

82.8 

99-3 

5-9 

132-4 

149.0 

182.  i 

41 

16.58 

33-16 

49-74 

66.3 

82.9 

99-5 

6.1 

132-6 

149.2 

182.4 

41 

42 

16.61 

33-22 

49.82 

66.4 

83.0 

99-  6 

6-3 

132.9 

149-5 

182.7 

42 

43 

16.64 

33-27 

49.91 

66.5 

83.2 

99.8 

6.4 

I33-I 

149-7 

183.0 

43 

44 
45 

16.66 
16.69 

33-33 
33-38 

50.00 
50.07 

66.6 
66.8 

83-3 
83-4 

00.0 

6.6 

6.8 

•33-3 
133-5 

150.0 

150   2 

183-3 
183-6 

44 
45 

46 

16.72 

33-44 

50-15 

66.9 

83.6 

00.3 

0 

133-7 

150.5 

183-9 

46 

47 

16.74 

33-49 

50.24 

67.0 

83.7 

oo.  5 

2 

150.7 

184.2 

47 

48 

16.77 

33-54 

50.32 

67.1 

83-9 

00.6 

4 

134-2 

151.  o 

184.5 

48 

49 

1  6.  80 

33-  60 

50.40 

67.2 

84.0 

00.8 

6 

134-4 

151-2 

,84.8 

49 

50 

16.83 

33-66 

50.-48 

67-3 

84.1 

OI.  O 

8 

.34-6 

151-4 

185.1 

50 

51 

16.86 

33-71 

50-56 

67-4 

84-3 

0      I 

8.0 

134-8 

151-7 

185.4 

5« 

52 

16.88 

33-76 

50-65 

67-5 

84.4 

o  -3 

8.  2 

135-  i 

151.9 

185.7 

5* 

53 

16.91 

33-82 

50.73 

67.6 

84.6 

o  -5 

8.4 

135-3 

152.2 

186.0 

53 

54  • 

16.94 

33-  87 

50.81. 

67.8 

84.7 

8.6 

135-5 

152.4 

186.3 

54 

55 

16.96 

33-93 

50.89 

67-9 

84-8 

o  .8 

8.8 

«35-7 

186.6 

55 

56 

16.99 

33-98 

50.98 

68.0 

85-0 

03.0 

8.9 

"35-9 

152.9 

186.9 

56 

Si 

17.02 
17.05 

34-04 
34-09 

51-06 
51.14 

68.1 
68.2 

85.1 
85-2 

02.  1 
02.3 

9.1 
9-3 

•  36.2 
136.4 

153.2 
153-4 

187.2 
•87.5 

57 
58 

59 

,7-08 

34-16 

51-24 

68.3 

85-4 

02.5 

9-5 

136.6 

153-7 

,87.9 

59 

Horz. 

97-28 

194.6 

291-9 

389-2 

486.4 

584 

68  1 

778 

876 

1070 

Horz. 

Dist. 

DisU 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .095  ft.  to  each   100  ft.  of 
distance  for  each  10'  departure. 


82 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES    IN    ELEVATION 
10° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

t 

0 

17.  10 

34-20 

5  -30 

68.4 

85- 

102.6 

•9-7 

36.8 

!53-  9 

1  88.  i 

I 

17-  13 

34-26 

5  -39 

68.5 

85- 

102.  8 

19.9 

37-o 

154-2 

188.4 

2 

17.16 

34-3' 

5  -47 

68.6 

85- 

102.  9 

20.  1 

37-2 

154-  4 

188.7 

3 

17.18 

34-37 

5  -55 

68.7 

85- 

103.1 

20.3 

37-5 

154-6 

189.0 

4 

17.21 

34-42 

5  -63 

68.8 

86. 

103.3 

20.5 

37-7 

154.9 

189-3 

5 

17-24 

34-48 

5  -7i 

69.  o 

86. 

103.4 

20.7 

37-9 

155-  « 

189.6 

6 

17.26 

34-53 

5  80 

69.1 

86.3 

103.6 

20.9 

38.1 

155-4 

189.9 

7 

17.29 

34-58 

5  ^88 

69.2 

86.5 

103.8 

2  .0 

38.3 

155-6 

190.  2 

8 

17-32 

34-64 

5  -96 

69.3 

86.6 

103.9 

2  .2 

38.6 

155-  9 

190-  5 

9 

17-35 

34-69 

5  -04 

69-4 

86.7 

104.1 

2  -4 

38-8 

156-1 

190.8 

c 

17-37 

34-75 

5  -12 

69-5 
60  6 

86.9 

Q-  n 

104.2 

2  .6 

39-o 

156.4 

191.  i 

1 

12 

17.  4° 
17-43 

34^86 

5  *  20 
5  -29 

69:7 

07.  o 

87.1 

104.6 

2  .0 

39-4 

156.6 
156-9 

191.  4 
191.7 

1 

13 

17-46 

34-91 

5  -37 

69.8 

87.3 

104.7 

2  .  2 

39-6 

157-  I 

192.  P 

3 

17-48 

34-97 

5  -45 

69.9 

87.4 

104.9 

2  .4 

39-9 

157-4 

192.3 

4 

'5 

17-51 

35-02 

5  -53 

70.0 

87.6 

105.1 

2  .6 

40.  i 

157-6 

192.6 

5 

16 

17-54 

35-o8 

5  -61 

70.2 

87.7 

105-  2 

22.8 

40-3 

157-8 

192.9 

6 

'7 

•7-56 

35  13 

5  -70 

70.3 

87.8 

105.4 

23.  o 

40-5 

158.  l 

'93-  2 

7 

18 
19 

17-59 
17.62 

35-18 
35-24 

5  -78 
5  -86 

70.4 
70.5 

88.0 
88.1 

105.6 

105.7 

23.1 
23-3 

40.7 
41.0 

Si 

193-5 
193-8 

18 
•9 

20 

17-65 

35-29 

52-94 

70.6 

88.2 

105.9 

23-5 

41.2 

158.8 

194.1 

20 

21 

17-67 

35-35 

53-02 

70.7 

88.4 

106.0 

23-7 

41.4 

159.' 

194-4 

2I 

22 

17.70 

35-40 

53-  10 

70.8 

88.5 

106.2 

23-9 

1.6 

159-3 

194-  7 

22 

23 

17-73 

35.46 

53-18 

70.9 

88.6 

106.4 

24.1 

1.8 

159-6 

195-0 

23 

24 

17-76 

35-51 

53-27 

71.0 

88.8 

106.5 

24-3 

2.0 

159.8 

•95-3 

24 

25 

17.78 

35.56 

53-35 

jri.l 

88.9 

106.7 

24-5 

2-3 

160.0 

195-6 

25 

26 

f7.8i 

17  84 

35-62 
35-  67 

53-43 

71.2 

89.  o 

106.  9 

24-7 

2.5 

160.3 

'95-9 

26' 

28 

17'  86 

35-73 

53-  51 
53-59 

71-5 

89-3 

107.2 

25.0 

42.9 

1  60.  5 
160,  8 

196.  2 
196.5 

27 
28 

29 

17-89 

35.78 

53-67 

71.6 

89-5 

107.4 

25-2 

43-  i 

16  .0 

196.8 

29 

30 

17.92 

35.84 

53-76 

7i-7 

89.6 

107-5 

25-4 

43-4 

16  .3 

197.  I 

30 

31 

17-95 

35.89 

53-  84 

71-8 

89-7 

107.7 

25.6 

43-6 

16  .5 

197-4 

31 

32 

17-97 

35-94 

53-92 

7i-9 

89.9 

107.8 

25.8 

43-8 

16  .8 

197-  7 

32 

33 

18.00 

36.00 

54.00 

72.0 

90.0 

108.  o 

26.0 

44-0 

16  .  o 

198.0 

33 

34 

18.03 

36-05 

54.08 

72-  i 

90.  i 

108.  2 

26.2 

44-2 

162.2 

198.3 

34 

35 

18.05 

36.11 

54-  -6 

72-2 

90-3 

108.3 

26.4 

44-4 

162.5 

198.6 

35 

36 

18.08 

36.  6 

54-24 

72-3 

90.4 

108.5 

26.6 

44-6 

162.7 

198.9 

36 

37 

1  8.  II 

36.  2 

54-33 

72.  4 

90.5 

108.  6 

26.8 

44-9 

163.0 

199.2 

38 

18.14 

36.  7 

54-41 

72.5 

90.7 

108.8 

27.0 

45-  i 

163.2 

199-5 

38 

39 

18.  16 

36.  2 

54-49 

72.6 

90.8 

109.0 

27.  i 

45-3 

163.5 

,99.8 

39 

40 

18.19 

36.  8 

54-57 

72.8 

109.  I 

27-3 

45-5 

.63.7 

200.  I 

40 

41 

18.  22 

36.  3 

54-65 

72.9 

., 

109-3 

27-5 

45-7 

164.0 

200.4 

41 

42 

18.24 

36.  9 

54-73 

73-0 

,  2 

109.  5 

27-7 

46.  o 

164.2 

200.  7 

42 

43 

18.27 

36.54 

54-81 

73-  i 

•4 

109.  6 

27-9 

46.2 

164-4 

201.0 

43 

44 

18.30 

36.60 

54-89 

73-2 

•  5 

109.8 

28.  i 

46.4 

164.7 

201.  3 

44 

45 
46 

18.32 

36.65 

54-98 
55-  06 

73-3 

.6 

28.3 

46.6 

164.9 

201.6 

45 

47 
48 

Is:  38 
18.  41 

36^76 
36-81 

55-14 

55-22 

73-5 
73-6 

9 

2.0 

110.3 
110.4 

28.6 
28.8 

47-2 

165.  4 
165.6 

202.  2 
2O2.  5 

47 
48 

49 

18.43 

36.87 

55-30 

73-7 

92.2 

29.0 

47-5 

165-9 

49 

50 

18.46 

36.92 

55-38 

73-8 

92-3 

no.  S 

29.2 

47-7 

166.1 

203.1 

50 

51 

18.49 

36.98 

55.46 

74-0 

92.4 

no.  9 

29.4 

47-9 

166.4 

203.4 

51 

52 

18.51 

37-03 

55-54 

74-  i 

92.6 

in.  i 

29.6 

48.1 

1  66.  6 

203.7 

52 

53 

18.54 

37-oS 

55-62 

74-2 

92.7 

III.  2 

29.8 

48.3 

166.9 

204.0 

53 

54 

18.57 

37-14 

55-71 

74-3 

92.8 

111^4 

30.0 

48.6 

167.1 

204.  2 

54 

55 

18.  60 

37-19 

55-79 

74-4 

93-° 

in.  6 

30.2 

48.8 

167.4 

204.6 

55 

56 

18.62 

37-24 

55-87 

74-5 

93-1 

in.  7 

30.4 

49.0 

167.6 

204.8 

56 

57 

18.65 

37-30 

55-95 

74-6 

93-2 

111.9 

30.  6 

49-2 

167.8 

205.  I 

57 

58 

18.68 

37-35 

56-03 

74-7 

93-4 

112.  I 

30.7 

49-4 

1  68.  i 

205.4 

58 

59 

18.70 

37-41 

56-11 

74-8 

93-5 

112.  2 

30.9 

49-6 

168.3 

205.7 

59 

Horz. 
t)ist. 

96.68 

«93-4 

290.0 

386.7 

483.4 

580 

677 

773  . 

870 

1064 

Horz. 
Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .105  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC   STADIA.  SURVEYING 


S3 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
11° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

f 

o 

i8.73 

37-46 

56.19 

74-9 

93-6 

12.4 

i3«-« 

149.8 

168.6 

206.0 

O 

I 

18.76 

37-52 

56.27 

75-0 

93-8 

12.6 

I3I-3 

150.  i 

168.8 

206.  3 

I 

1 

18.78 

37-57 

56.36 

75-  ' 

93-9 

12.7 

13'-  5 

150.3 

169.1 

206.6 

a- 

3 

18.  81 

37.62 

56.43 

75-2 

94-  i 

12.9 

«3'.7 

150.5 

169.3 

206.9 

3 

4 

18.84 

37.68 

56-5. 

75-4 

94.2 

13.0 

131-9 

150-7 

169.5 

207.  2 

4 

5 

1  8.  86 

37-73 

56.60 

75-5 

94-3 

13-2 

132.1 

i50-9 

169.8 

207.5 

5 

6 

18.89 

37-78 

56.68 

75-6 

94-5 

'3-4 

132-2 

'5  ' 

170.0 

207.8 

6 

7 

18.92 

37-84 

56.76 

75-7 

94.6 

'3-5 

132.4 

15  4 

170.3 

2Q8.I 

7 

8 

.8.95 

37-89 

56.84 

75-8 

94-7 

13.7 

132-6 

15  6 

170.5 

208.4 

8 

9 

18.97 

37-95 

56.92 

75-9 

94-9 

13-8 

132-8 

15  8 

170.8 

208.7 

9- 

10 

19.00 

38.00 

57-oo 

76.0 

95-o 

14.0 

«33-o 

15  o 

171.0 

209.0 

to 

II 

'9-03 

38-05 

57.08 

76.1 

95-  1 

14.2 

133-2 

15  2 

171.2 

209.3 

ii 

2 

'9-°5 

38.11 

57-16 

76.2 

95-3 

14-3 

133-4 

15  4 

i7i-5 

209.  6 

12 

3 
4 

19.08 
19.  u 

38.  1  6 
38.22 

57-24 
57-32 

76.3 
76.4 

95-4 
95-5 

'4-5 
14-6 

J33-6 
133-8 

15  6 

171.7 

269.9 

13 
14 

5 
6 

19-13 
19.  6 

38.27 
38.32 

57-40 
57-48 

76:5 
76.6 

95-7 

95-8 

14.8 
15.0 

133-9 
134-1 

153-3 

172-4 

2  0.8 

15 

16 

7 

19.  9 

38.38 

57-56 

76.8 

95-9 

'5-  ' 

134-3 

153-5 

172-7 

2  I.  I 

»7 

18 

19.  2 

38.43 

57-64 

76-  9 

96.1 

'5-3 

134-5 

153-7 

172.9 

2  1.4 

18 

«9 

19.  4 

38.48 

57-72 

77-o 

96.2 

15-4 

134-7 

153-9 

173-2 

2  I.  7 

19 

30 

19.  7 

38.54 

57-81 

77-  ' 

96.3 

J5-6 

134-9 

154-2 

173-4 

2  2.0 

20 

31 

I9.30 

38.59 

57-89 

77.  a 

96-5 
06  6 

15-8 

'35-1 

154-4 

173-7 

2  2.  2 

21 

»3 

19.  32 
19-35 

38.  64 
38.70 

57-  97 
58-05 

77-  3 

77-4 

9^8 

\6.i 

135-4 

•  54-8 

174.  i 

2  2.8 

23 

24 

19.38 

38.75 

&;? 

77-5 

96.9 

16.3 

135-6 

155-0 

174-4 

2  3-1 

24 

25 

36 

19.  40 
'9-43 

38.  8O 

38.86 

5».  21 
58.29 

77-  6 

77-7 

97.0 

97.2 

16.4 
16.  6 

135-  8 
136.0 

155-4 

174-9 

2  3-7 

26' 

27 

19.46 

38.91 

58.37 

77-8 

97-3 

16.7 

136.2 

155-6 

i75-i 

2  4.0 

27 

28 

19.48 

38.97 

58-  45 

77-9 

97-4 

16.9 

136.4 

155-9 

175-4 

2  4-3 

28 

29 

i9-5> 

39-02 

58-53 

97-  6 

17.  i 

136.6 

i«6.  i 

175-6 

2  4.6 

29 

30 

'9-54 

39-07 

58.61 

7^2 

97-7 

17.2 

136-8 

156-3 

175-8 

2  4-9 

30 

3i 

19.56 

39-  '3 

58.69 

78.2 

97-8 

17-4 

136-9 

IS6.5 

176.1 

2  5.  2 

3« 

32 

'9-59 

39-  "8 

58.77 

78.4 

98.0 

'7-5 

137-  i 

156.7 

176.3 

2  5-5 

32 

33 

19.62 

39-23 

58.85 

78.5 

98.1 

17-7 

137-3 

156.9 

176.6 

2  5-8 

33 

34 

19.64 

39-29 

58.93 

78.6 

98.2 

J7-9 

137-5 

157-2 

176.8 

2  6.  I 

34 

35 

19.67 

39-34 

59-01 

78.7 

98-4 

137-7 

«57-4 

i77-o 

2  6.4 

35 

36 

19.70 

39-39 

59-09 

78.8 

98.5 

1  8.  a 

137-9 

157-6 

177-3 

2  6.7 

36 

37 

19.72 

39-45 

59-  '7 

78.9 

98.  6 

18.3 

138.1 

157-8 

177-5 

2  7.  O 

37 

38 

"9-75 

39-50 

59-  25 

79.0 

98.8 

18.5 

138.2 

158.0 

177.8 

2  7-3 

38 

39 

19.78 

39-56 

59-33 

79.1 

98.9 

18.7 

138.4 

158-2 

178.0 

2  7.6 

39 

40 

19.  80 

39-61 

59-4' 

79-2 

99.0 

1  8.  8 

138.6 

158-4 

178.2 

2  7.8 

40 

4« 

19.83 

39-66 

59-49 

79-3 

99.2 

19.0 

138.8 

.58.6 

178-5 

2  8.  1 

4> 

42 

.9.86 

39-72 

59-57 

79-4 

99-3 

19.2 

139-0 

158.9 

178-7 

3  8.  4 

42 

« 

19.88 

39-77 

59-65 

79-5 

99-4 

19-3 

139-2 

159-1 

179.0 

2  8.7 

43 

44 

19.  91 

39-82 

59-73 

79-6 

99-6 

19-5 

139-4 

159-3 

179.2 

2  9.0 

44 

45 

19.94 

39.88 

59-81 

79-8 

99-7 

19.6 

139-6 

159-5 

179-4 

2  9-3 

45 

46 

19.96 

39-93 

59-89 

79-9 

iS'o 

19-8 

.39-8 

159-7 

179-7 

2  9.  6 

46 

47 

19.99 

39-98 

59-97 

80.0 

20.  o 

139-9 

159-9 

179.9 

2  9-9 

47 

48 

20.02 

40-04 

60.  05 

80.  I 

100.  I 

20.  I 

140.1 

160.  i 

180.2 

2  0.  2 

48 

50 

2O.O7 

40.14 

60.21 

80.3 

100.4 

20.  4 

140.5 

160.6 

180.6 

50 

5' 

20.  IO 

40.20 

60.  29 

80.4 

100.5 

20.6 

140.7 

160.8 

,80.9 

2  I.  I 

5« 

5» 

20.  12 

40.25 

60.  37 

80.5 

loo.  6 

20.  7 

140.9 

16  .0 

18  .1 

2  I.  4 

52 

53 

20.15 

40.30 

60.45 

80.6 

loo.  8 

20.9 

141.0 

16  .2- 

18  .  4 

2  1.7 

53 

54 

20.18 

40.36 

60.53 

80.7 

100.9 

2  .  I 

14  .2 

16  .4 

18  .6 

2  2.0 

54 

55 

2O.  2O 

40.41 

60.  6  1 

Rr»  n 

18  1 

55 

cfi 

56 
57 

2O.  23 
20.  26 

40.  46 
4°-  51 

60.  77 

oo.  9 

8l.O 

101.3 

2  •  5 

14  -8 

16  .1 

is  :3 

222!  8 

5° 
57 

58 
.  59 

30.28 
20.  31 

40-57 
40.  62 

60.85 
60.93 

81.  I 

™'.6 

2  -7 

14  .0 

14  .2 

16  .3 
16  .5 

18  .6 
18  .8 

223.  I 
223.4 

58 
59 

Horz. 
Dist 

96.03 

192.  i 

288., 

384-' 

480.2 

576 

672 

768 

864 

I056 

Horz. 
Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .113  ft.  to  each  TOO  ft.  of 
distance  for  each  10'  departure. 


84 


TOPOGRAPHIC   STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
12° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

/ 

0  - 

20-34 

40.67 

61  .  01 

8  -3 

101.7 

122.0 

142. 

162.7 

183.0 

2  3-7 

I 

20.36 

40-73 
40.  78 

6  .09 

•  4 

101.8 

122.  2 

142.. 

162.9 

163.    I 

183.3 

2    4.0 

3 

20'  42 

40.83 

6  .25 

•7 

102.  I 

122-5 

142.  » 

163-3 

183^7 

2  4^6 

4 

20.44 

40.89 

6-33 

.8 

102.  2 

122.7 

MS- 

163-5 

184.0 

2    4.9 

"5 

20.47 

40.94 

6  .41 

•  9 

102-4 

122.8 

MS- 

163.8 

184.2 

2    5.  2 

6 

20.50 

40.99 

6  .49 

8  .0 

102.5 

123.0 

M3- 

:64.o 

184,  5 

225-5 

7 

20.  52 

41.04 

6.57 

8  .1 

102.6 

I23.I 

143- 

164.2 

184.7 

.0.     n 

"5.8 

9 

20.  58 

41-  15 

6  .73 

8  -3 

102.9 

123.  3 
123-4 

M3- 
144. 

164.  4 

164.6 

104.9 

185.  2 

226.  3 

10 

20.  60 

41.20 

6  .81 

82.4 

IO3.O 

123.6 

144. 

164.8 

•85.4 

226.6 

I 

,, 

20.63 

41.26 

6  .89 

82.5 

103.  I 

123.8 

144. 

165.0 

185.7 

226.9 

i 

12 

20.66 

4I-31 

6  .  97 

82.6 

«o3-3 

123-9 

144. 

165.2 

185.9 

227.2 

i 

13 

20.68 

4I-36 

6  .04 

82.7 

.103-  4 

124.1 

144. 

165.4 

186.1 

227-5 

I  < 

>4 

20.71 

41.42 

6    .12 

82.8 

Q~    0 

103-  5 

124.2 

MS- 

165.7 

186.4 

1; 

'5 
16 

20.  73 
20.76 

41.  47 

41-52 

62.28 

02.  9 

83.0 

103.  8 

124.6 

MS-  3 

166.  i 

1  86.  8 

228.4 

16 

•7 

20.79 

41-58 

62.36 

83.2 

103.9 

124.7 

MS-  5 

166.3 

187.1 

228.  7 

17 

18 

20.81 

41.63 

62.44 

83.3" 

104.1 

124.9 

MS-  7 

166.5 

187-3 

229.9 

18 

>9 

20.84 

4..  68 

62.52 

83-  4~ 

104.2 

125.0 

1  45-  9 

166.7 

187.6 

229.  2 

19 

20 

20.87 

4'-73 

62.60 

83-5 

104.3 

125.2 

146-1 

166.9 

187.8 

229-5 

20 

21 

20.  89 

41.79 

62.68 

83-6 

104-5 

.125-4 

146.2 

167.2 

188.0 

229.8 

21 

22 

20.92 

41.84 

62.76 

83-7 

104.6 

125-5 

146.4 

167-4 

188.3 

230.1 

22 

23 

20.95 

41.89 

62.  84 

-83-8 

104.7 

125-7 

r46.6 

167.6 

.88.5 

230.4 

23 

24 

20.97 

41.94 

62.92 

83-9 

104.9 

125.8 

146.8 

167.8 

188.8 

230.7 

24 

26 

2    .03 

42.05 

63.08 

84.1 

105.1 

126.2 
lift  i 

M7-2 

168.2 

1  68  4 

189.2 

|«n      r 

III 

26 

38 

2.08 

42.  j  6 

63-23 

84-3 

105.  3 
J05-4 

120.  3 

126.5 

•147-4 
147-6 

168.6 

109-  5 
189-7 

23  .  o 
23  -9 

27 

29 

2    .  10 

42.21 

63-31 

84.4 

105.5 

126.6 

M7-  7 

168.8 

189.9 

23   .2 

29 

3° 

2    .13 

4.2J6 

63-39 

84-5 

105-7 

126.8 

M7-9 

169.0 

190.2 

23  -4 

30 

31 

21.16 

42.  32 

63-47 

84.6 

105.8 

127.0 

148.1 

169.3 

190.4 

232.7 

3 

32 

2I.I8 

42-37 

63-55 

84-7 

105.9 

127.  1 

M8.3 

169-5 

190.6 

233-0 

32 

33 

21.21 

42.42 

63-63 

6l    71 

84.8 
S5  o 

106.0 

127.3 

148.5 

169.7 

190.9 

233-3 

33 

35 

21^26 

42.52 

03-  /' 
63.79 

85.0 

106.3 

127.6 

148.8 

170.1 

191.4 

233-9 

.34 
35 

36 
37 

21.  »9 
21.32 

42-  5»- 

42.63 

63.87 
63-95 

85.2 

85-3 

106.4 
106.6 

127.7 
127-9 

149.0 
149.2 

170.3 
170.5 

191-6 
191.8 

234-2 
234-5 

36 
37 

38 

21-34 

42.68 

64.02 

85.4 

106.7 

128.0 

149.4 

170.7 

192.1 

234-8 

38 

39 

21-37 

42.74 

64.  10 

ft*    iR 

85.5 

oe    f. 

106.8 

149-6 

170.9 

192.3 

235-0 

39 

41 

21.  39 
21.42 

42.  79 
42.84 

04.  IB 
64.26 

05.  O 

85-7 

107.  l 

128.5 

149-9 

171. 

192.6 
192.8 

235-3 
235-6 

4O- 
41 

42 

21-45 

42-89 

64.34 

85.8 

107.2 

128.7 

150.  i 

171. 

193-0 

235-9 

42 

43 

21.47 

42-95 

64.42 

85-9 

107.4 

128.  8 

150-3 

171. 

193-3 

236.2 

43 

44 

21.50 

43.00 

64.50 

86.0 

107-5 

129.0 

150.5 

I?2. 

193-5 

236.5 

44 

45 

21-53 

43-05 

64.58 

86.1 

107.6 

129.2 

150.7 

172. 

193-7 

236.8 

45 

46 

21-55 

43-  JO 

64.66 

86.2 

107.8 

129-3 

150-9 

172. 

194-0 

237-1 

46 

47 

21.58 

43-16 

64-73 

86.3 

107-9 

129-5 

•  i5'-o 

172. 

194.2 

237-4 

47 

48 

21.60 

43-21 

64.81 

86.4 

108.0 

129.6 

151.  2 

172. 

194.4 

237  6 

48 

'49 

21.63 

43-26 

64.89 

86.5 

108.2 

129.  8 

15I-4 

173- 

194-7 

237-9 

49 

50 

21.66 

43-31 

64.97 

86.6 

108.3 

129-9 

I51-6 

173- 

194.9 

238.  2 

50 

51 

21.68 

43-37 

65.05 

86.7 

108.4 

130.1 

.51.8 

173- 

195-2 

238.5 

5' 

5* 

21.71 

43-42 

65.13 

86.8 

108.6 

130-2 

152.0 

173- 

195-4 

238.8 

52 

53 

21-74 

43-47 

65.21 

86.9 

108.7 

130.4 

152.2 

173- 

195.6 

239-1 

53 

54 

21.76 

43-52 

65-28 

87.0 

1  08.  8 

130.6 

152.3 

174- 

195-8 

239-4 

54 

55 

2J-79 

43-58 

65.36 

87.2 

108.9 

130.7 

152.5 

•74- 

196.1 

239-7 

55 

56 

21.81 

43-63 

65.44 

87-3 

109.1 

130.9 

152.7 

174-5 

196.3 

240.0 

56 

57 

21.84 

43-68 

65.52 

87-4 

109.2 

131.0 

152.9 

174-7 

196.6 

240.2 

57 

58 

21.87 

43-73 

65.60 

87-5 

109-3 

131-2 

I53-I 

174-9 

196.8 

240.5 

5« 

59 

21.89 

43-78 

65.  68 

87.6 

109-5 

I3I-4 

153-2 

I75-I 

197-0 

240.  8 

59 

Horz. 

Dist. 

95-32 

190.6 

286.0 

381.3 

476.6 

572 

667 

763 

858 

1048 

Hon. 
Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .123  ft.  to  each   100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC   STADIA  SURVEYING 


85 


TABLE  7 — Continued 

DIFFERENCES   IN    ELEVATION 
13° 


f 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

/ 

o 

21.92 

43-84 

65.76 

87.7 

109.6 

131-5 

153-4 

175-4 

197-3 

241.1 

x 

21.94 

43-89 

65-83 

87.8 

109.7 

131-7 

153-6 

175-6 

197.5 

241.4 

2 

21.  97 

43-94 

65.91 

87.9 

09.9 

131-8 

153-8 

•75-8 

197-7 

241.7 

3 

22.00 

43-99 

65-99 

10.  0 

132-0 

154.0 

176.0 

198.0 

242.0 

4 

22.02 

44-05 

66.07 

88.  i 

1O.  1 

132-1 

154-2 

176.2 

198.2 

242.2 

5 

22.05 

44.10 

66.15 

88.2 

10.  2 

132-3 

154-3 

176.4 

198.4 

242.5 

6 

.22.08 

44-  >5 

66.23 

88.3 

10-4 

132-4 

154-5 

176.6 

198.7 

242.8 

7 

22.  10 

44-20 

66.30 

88.4 

10-5 

132-6 

154-7 

176.8 

198.9 

243.  1 

8 

22.13 

44.26 

66.38 

88.5 

132.8 

154-9 

177.  ° 

199.  2 

243.4 

8 

9 

22.  15 

44-3' 

66.46 

88.6 

10.  8 

132.9 

155-1 

177.2 

199.4 

243.7 

9 

22.  18 

44-3* 

66.54 

88.7 

10.9 

"33-1 

155.3 

177-4 

199.6 

10 

, 

22.  21 

44.41 

66.62 

88.8 

II.  O 

>33-2 

155-4 

177.6 

199.8 

244.3 

n 

2 

22.23 

44-  46 

66.70 

88.  9 

1  1.  2 

133-4 

155-6 

177-9 

2OO.  I 

244.6 

12 

3 

22.  26 

44-52 

66.77 

89.  o 

"•3 

133.6 

155-8 

178.  i 

200-3 

244.8 

J3 

4 

22.28 

44-57 

66.  85 

89.1 

11.4 

133-7 

156.0 

178-3 

200.  6 

245.1 

U 

5 

22.31 

44.62 

66.93 

89.2 

n.  6 

133-9 

156-2 

178-5 

200.  8 

245.4 

15 

6 

22.34 

44.67 

67.01 

89.3 

11.7 

134.0 

156.4 

178.7 

201.0 

245.7 

16 

7 

22.  36 

44-72 

67.09 

-  89.4 

n.  8 

134-2 

156-5 

178.9 

201.3 

246.0 

17 

18 

22.39 

44-78 

67.  1  6 

89.6 

u.g 

134-3 

156.7 

179.  i 

201.5 

246.3 

18 

19 

22.41 

44.83 

67.24 

89.7 

12.  I 

134-5 

156.9 

179-3 

201.  7 

246.6 

19 

20 

22.44 

44-88 

67-32 

89.8 

12.  2 

"34-6 

«57-  1 

179-5 

202.0 

246.8 

20 

21 

22.47 

44-93 

67.40 

89.9 

12-3 

134-8 

157-3 

179-7 

202.  2 

247.  1 

21 

22 

22-49 

44.98 

67.48 

90.0 

12-5 

135-0 

157-4 

179.9 

2O2.  4 

247.4 

22 

23 

22.52 

45-04 

67-55 

90.1 

12.6 

135-1 

157-6 

1  80.  i 

202-7 

247.7 

23 

24 

22.54 

45-09 

67.63 

9°-  2. 

I2.7 

135-3 

157.8 

180.4 

202.9 

248.0 

24 

25 

22-57 

45-  '4 

67.71 

9°-3 

12.8 

135-4 

.158-0 

180.6 

203.  I 

248.3 

25 

26 

22.60 

45-  "9 

67.79 

90.4 

13.0 

135-6 

158.2 

180.8 

203.4 

248.6 

26 

27 

22.62 

45-24 

67.86 

90.5 

13.  I 

135-7 

158.4 

181.0 

203.  6 

248.8 

27 

28 

22.  65 

45-30 

67.  94 

90.  6 

13.2 

135-9 

158-5 

181.2 

203.8 

249.  1 

28 

29 

22.67 

45-35 

68.02 

90.7 

'3-4 

136.0 

158.7 

181.4 

204.  i 

249.4 

29 

30 

22.  70 

45-40 

68.  10 

90.8 

'3-5 

136-2 

158.9 

181.6 

204.3 

249-7 

30 

31 

22-73 

45-45 

68.18 

90.9 

13-6 

136.4 

I59-I 

181.8 

204.5 

250.0 

31 

32 

22.75 

45-50 

68.  25 

9  -0 

13-8 

136.5 

159-3 

182.0 

204.  8 

250.3 

32 

33 

22.78 

45-55 

68-33 

9  •  i 

"3-9 

136.7 
136.  8 

159-4 

l82.  2 

205.0 

250.  6 

33 

34 
35 

22.83 

45.66 

68.49 

9  -3 

14.1 

137-0 

159'  8 

182^6 

205.5 

251.  i 

35 

36 

22.86 

45-  7  1 

68.56 

9  -4 

'4-3 

137-1 

160.0 

182.8 

205.7 

25I-4 

36 

37 

22.88 

45-76 

68.64 

9  -5 

14.4 

137-3 

160.  2 

183.0 

205.9 

251-7 

37 

38 

22.91 

45.8i 

68.72 

9  -6 

14.5 

137-4 

160.4 

183.2 

206.  2 

252.0 

38 

39 

22.94 

45.88 

68.81 

9  -8 

14.  7 

137-6 

160.  6 

183.5 

206.4 

252-3 

39 

40 

22.96 

45-92 

68.88 

9  -8 

14-8 

137-8 

160.7 

I83-7 

206.6 

252-5 

40 

4i 

22.  98 

45-97 

68.95 
fiQ  ni 

91.9 

14-9 

137-9 
1181 

160.9 
161.  i 

183.9 

ISA         I 

206.9 

252-8 

41 

43 

23-04 

46.07 

09.  03 

69.11 

92.  i 

15.  o 
"5-2 

130.  i 
138-2 

161.2 

1840 

207-3 

253.  i 
253-4 

43 

44 

23.06 

46.12 

69.  1  8 

92.2 

15.3 

138.4 

161.4 

184.5 

207:6 

253-7 

44 

45 

23-09 

46.18 

69-26 

92-4 

15.4 

'38.5 

161.6 

184.7 

207.  8 

254-0 

45 

46 
47 

23.11 

23-  '4 

46-23 

46.28 

69-34 
69.42 

92.4 
92.6 

'5.6 
"5-7 

138-7 

.38.8 

161.8 
162.0 

184.9 
I85-I 

208.0 
208.2 

254-2 
254-5 

46 

47 

48 

23-  '5 

46.30 

69.46 

92.6 

138.9 

162.  i 

185.2 

208.4 

254-7 

48 

49 

23-  '9 

46.38 

69.57 

92.8 

16.  o 

I39-I 

162.3 

185-5 

208.7 

255-1 

49 

50 

23-22 

46.43 

69.65 

92.9 

16.  i 

139-3 

162.5 

185.7 

209.0 

255-4 

5« 

Si 

23-24 

46.48 

69-73 

93-o 

16.  2 

139-4 

162.7 

185.9 

209.2 

255-7 

5' 

52 

23-27 

46.54 

69.81 

93-1 

16.3 

I39.  6 

162.9 

209.4 

256.0 

52 

53 

23.29 

46.59 

69.88 

93-2 

16.5 

139.8 

163.0 

186.4 

209.6 

256.2 

53 

54 

23-32 

46.64 

.69.96 

93-3 

16.  6 

139-9 

163.2 

186.6 

209.9 

256.5 

54 

55 
56 

23  34 

46.69 
46.  74 

70.04 

93-4 

16.7 
ifi  o 

163-4 

186.8 

256.«8 

55 
56 

57 

58' 

23-40 
23-42 

46.79 
46.84 

70.  19 
70.37 

93-  5 
93-6 
93-7 

10.  9 
17.0 

17.  I 

140.4 
140.5 

163-8 
164.0 

187.  2 
187.4 

210.6 
210.8 

257-4 
257.6 

57 
5« 

59 

23-45 

46.  90 

70.34 

93-8 

17.  2 

140.  7 

164.1 

I87.6 

211.  0 

257-9 

59 

Horz 

94-55 

189.1 

283.6 

378.2 

472.8 

567 

662 

756 

851 

1040 

Horz. 

Dist. 

Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .132  ft.  to  each  100  ft.  of 
distance  for  each  10'  departure- 


86 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
14° 


/ 

100 

200 

300 

400 

500 

600. 

700 

800 

900 

1100 

f 

0 

23-47 

47.00 

70.  42 

93-9 

J'7-4 

140.8 

164-3 

187.8 

211.3. 

258.2 

0 

4, 

23-50 

47-00 

70.  50 

94-0 

117-5 

141.0 

164.5 

188.0 

211.5 

258.5 

,CQ      Q 

1 

3 

23-  52 
23-55 

47.05 
47.10 

70.58 
70.  65 

94-  l 
94.2 

"7!  a 

I4J-3 

164.8 

188.4 

212.0 

250.  o 

259.' 

3 

4 
5 

23-  58 
23.60 

47-  '5 
47.20 

70.  73 
70.81 

94-  3 
94-4 

I    7-  9 
llS.O 

141.  5 
141.6 

165.2 

188.8 

212.4 

259.6 

4 
5 

6 

23-63 

47.25 

70.88 

94-5 

118.  i 

.  ,0     , 

,41.* 

165-4 

,/   -     A 

189.0 

212.6 

259.9 

6 

I 

23-  65 

23.68 

47-  3* 

47-36 

70.  96 
71.04 

94-  6 
94-7 

I  lo.  3 

142.1 

105.  D 
165.8 

189.4 

213.  I 

260.5 

8 

9 

23.70 

47-  4' 

71.  ii 

94.8 

1  1  8.  5 

142.2 

165.9 

189.6 

213-3 

260.8 

9 

10 

23-73 

47.46 

71.19 

94-9 

118.6 

142.4 

166.1 

189.8 

213.6 

261.0 

10 

II 

23-76 

47-  5« 

71.27 

95-0 

1  1  8.  8 

142.5 

166.3 

190.0 

.213.8 

261.3 

|i 

12 

23-78 

47.56 

71-34 

95-  ' 

118.9 

142-7 

166.5 

190.2 

214.0 

261.6 

12 

>3 

23.81 

47.6i 

71.42 

95-2 

119.0 

142.8 

166.6 

190.5 

214-3 

261.9 

I* 

>4 

23-83 

47.66 

7I-50 

95-3 

119.2 

143.0 

166.8 

190.7 

2  4-5 

262.4 

14 

15 

23.86 

47-7* 

71-57 

95-4 

i  9-3 

143-2 

167.0 

190.9 

214-7 

262.4 

15 

16 

23.88 

47-77 

71-65 

95-5 

119.4 

143-3 

167.2 

19  .1 

215.0 

262.7 

16 

17 

23-91 

47-82 

71-73 

95-6 

119.6 

143-4 

167.4 

19  -3 

215-2 

263.0 

17 

18 
'9 

23-94 
23-96 

47-87 
47-92 

71.80 
71.88 

95'Z 
95-8 

119.7 
119.8 

143.6 
143-8 

167.5 
167.7 

19  -5 
19  .7 

215-4 
215-6 

SI 

18 
19 

20 

23-98 

47-97 

72.00 

95-9 

119.9 

143-9 

167.9 

19  -9 

215-9 

263.8 

2O 

31 

24.01 

48.02 

72-03 

96.0 

120.  I 

144.1 

I68.I 

19  .1 

216.  i 

264.1 

21 

22 

24.04 

48.07 

72.11 

96.2 

1  20.  ? 

144.2 

168.3 

19  -3 

216.3 

264.4 

it 

23 

24.06 

48.12 

72.19 

96.2 

120.3 

144.4 

168.4 

192-5 

216.6 

264.  7 

»3 

24 

24.09 

48.18 

72.26 

96.4 

1  20.  4 

144-5 

168.6 

192-7 

216.8 

265.0 

24 

25 

24.11 

48-23 

72-34 

96.4 

120.6 

J44-7 

168.8 

192.9 

217.0 

265.2 

15 

26 

24.14 

48.28 

72.42 

96.6 

120.7 

144.8 

169.0 

193-' 

217.2 

265.5 

*6 

27 

24.  i 

48.33 

72.49 

96.7 

120.  8 

'45-0 

169.2 

193-3 

217-5 

265.8 

27 

28 

24.1 

48.38 

72.57 

96.8 

121.0 

MS-  i 

169-3 

193-5 

217.  7 

266.1 

28 

»9 

24:2 

48.43 

72.64 

96-9 

121.  I 

145-3 

169-5 

193-7 

217-9 

266.4 

29 

30 

24.  2 

48.48 

72.72 

97-o 

121.  2 

M5-4 

169-7 

193-9 

218.2 

266.6 

3° 

3> 

24.2 

48.53 

72.80 

97-1 

121.  3 

145-6 

169-9 

194.1 

218.4 

266.9 

3« 

32 

24.  2 

48.58 

72.88 

97-2 

I2I.5 

145-8 

170.  o 

194-3 

218.6 

267.2 

3» 

33 

24-3 

48.63 

72.95 

97-3 

121.6 

145-9 

170.  2 

194-5 

218.8 

267.5 

33    . 

34 

24-34 

48.68 

73-03 

97-4 

121.  7 

146.0 

170.4 

194.7 

219.  i 

267.8 

34 

35 

24-37 

48.74 

73-io 

97-5 

121.  8 

146.2 

170.6 

194-9 

219-3 

268.0 

35 

36 

24-39 

48.79 

73-18 

97-6 

122.0 

146.4 

170.8 

195-' 

219-5 

268.3 

36 

37 

24.42 

48.84 

73-26 

97-7 

122.  I 

146-5 

170.9 

195-4 

219.8 

268.6 

37 

38 

24.44 

48.89 

73-33 

97-8 

122.2 

146.7 

I71.I 

195-6 

220.0 

268.9 

38 

39 

24.47 

48.94 

73-4' 

97-9 

122.4 

146.8 

I7I-3 

195.8 

220.  2 

269.2 

39 

.40 

»4-5<> 

48.99 

73.48 

98.0 

122-5 

147.0 

I7I-5 

196.0 

220.4 

269.4 

40 

4> 

24.52 

49.04 

73-56 

98.1 

122.6 

147.1 

I7I.6 

196.2 

220.7 

269.7 

4> 

42 

24-54 

49.09 

73.64 

98.2 

122.7 

1  47,-  3 

171.8 

196-4 

220.9 

270.0 

42 

43 

24-57 

49.14 

73-71 

98.3 

122.8 

147-4 

172.0 

196.6 

221.  I 

270.3 

43 

44 

24.60 

49.19 

73-79 

98.4 

123.0 

147.6 

172.2 

196,8 

221.4 

270.  6 

44 

45 

24-62 

49.24 

73.86 

98.5 

I23.I 

147-7 

172.  4 

197.0 

221.6 

270.8 

45 

46 

24-65 

49-29 

73-  94 

98-6 

23.2 

147.9 

172.5 

197.2 

221.8 

271.1 

46 

47 

24.67 

49-34 

74-02 

98.7 

23-4 

148.0 

172.7 

197-4 

222.  I 

271.4 

47 

48 

24.70 

49-39 

74.09 

98.8 

23-5 

148.  2 

172.9 

197-6 

222-3 

271.7 

48 

49 

24.72 

49-44 

74-17 

98.9 

23.6 

148.3 

I73-I 

197.8 

222.5 

272.0 

49 

50 

24-75 

49-50 

74-24 

99.0 

23-7 

148.5 

173-2 

198.0 

222.7 

272.2 

5° 

5' 

24.77 

49-55 

74-32 

99.1 

23-9 

148.6 

173-4 

'1  98.  2 

23-0 

272.5 

Si 

52 

24.80 

49.60 

74-39 

99.2 

24-0 

148.8 

173-6 

198.4 

23.2 

272.8 

52 

53 

24.82 

49-65 

74-47 

99-3 

24-1 

148.9 

173-8 

I98.6 

23-4 

273-1 

53 

54 

24-85 

49.70 

74-55 

99-4 

24.2 

149.1 

173-9 

198.8 

23.6 

273-3 

54 

55 

24.87 

49-75 

74.62 

99-5 

24.4 

149.2 

174.1 

199.0 

23-9 

273.6 

55 
cfi 

S6 
58 

24.90 
24.92 
24.95 

49-  80 
49-85 
49-  9° 

74.70 
74-77 
74.85 

99-  6 
99-7 
99-8 

124.6 

'  49-  6 
149-7 

174-5 
174-6 

199.4 
199.6 

224.3 
224.6 

274-  3 
274-4 

5° 
57 
58 

59 

24.98 

49-95 

74.92 

99-9 

124.9 

1  49-  8 

174.8 

199-8 

224-8 

274-7 

59 

Horz 
Dist. 

93-73 

J87.5 

374-9 

468.6 

562 

656 

750 

844 

1031 

Horz. 
Dist. 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .141  ft.  to  each   100  ft.  of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


87 


TABLE  7 — Continued 

DIFFERENCES    IN    ELEVATION 
15° 


t 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

f 

o 
I 

2 

3 

25-00 
25.02 
25-05 
25.08 

50.00 
50.05 
50.10 

75-oo 
75-08 
75-15 

100.0 
100.  2 

125.0 
125.2 
125.2 

150.0 
150-2 
150.3 

175-0 
175-2 
175-4 

200.0 

200.4 

225-3 
225-5 

275.0 

275-3 
275-6 

0 

4 
5 

6 

I 
9 

10 

ii. 

25.  10 
25-  '3 

*5-i5 
25.18 

25.  20 

25-23 

25.25 

S5-28 

50.  20 
50.25 

50.30 
50-35 
50.  40 
50-45 
50.50 

50.55 

75-30 
75.38 

75-45 
75-  53 
75.60 
75-68 
75-  76 

75-83 

100.  4 
100.5 

100.6 
100.7 

100.  9 

IOI.O 
101.  I 

J25-5 
125.* 

1*5-8 

"e'o 
126.1 

126.3 

126.4 

150.6 
150.8 

150.9 
15  • 
IS  • 
15  • 
15  • 

15  - 

175-7 
175-9 

176.0 
176.2 
176.4 
176.6 
176.8 

176.  9 

200.8 
201.0 

201.  2 
201.4 
201.  6 

202.0 

225.9 
226.1 

226.4 
226.  6 
226.8 
227.  o 
227.3 

276.  i 
276-4 

276.6 
276.9 
277.2 
277-5 
277.8 

4 
5 

6 

7 
8 
9 

10 

«3 
14 

25-30 
25-33 
25-35 

50.  60 
50-  65. 
50.70 

75-90 
75-98 
76.06 

101.  4 
101.  3 
101.4 

126.5 
126.6 
126.8 

15  • 
15  • 
15  • 

177.1 

177-3 
177-5 

202.6 

227.9 

278.3 
278.6 
278-9 

13 
•4 

15 

16 
17 
18 
"9 

20 

21 
22 

25-38 

25-40 
25-43 
25-45 
25-48 
25-50 

25-53 

25-  55 

50.75 

JO.  80 
50.85 
50.90 
50-95 

5I-05 

"76.13 

76.21 
76.28 
76.36 
76-43 
76.51 

76.58 
76.  66 

101.5 
101.6 

\l\.l 
101.9 

102.  1 
102.  2 

126.9 

127.0 
127.  I 
127.3 
127.4 
127.5 

127.6 

127.  8 

15  • 

15  • 
15  • 
15  • 
15  • 
153- 

153-2 
153-3 

177.6 

177-8 
178.0 

178^ 
178.5 

178.7 

203.2 
2°3-4 
203.6 
203.8 
204.0 

204.2 

228.6 
228.8 
229.1 
229.3 
229-5 

229-7 

279.  4- 
279.7 
280.0 
280.2 
280.  5 

280.8 
28  .1 

15 

16 
17 
18 
19 

20 

21 

22 

24 
25 

26 
27 
28 
29 

25-58 
25.60 
25-63 

25.65 
25.68 
25.70 
25-73 

5'-  '5 
51-  .0 
51-25 

51-30 
5>-35 
5'-40 
5'-45 

76.73 
76.81 
76.88 

76.95 
77-03 
77.11 
77.18 

102.3 
102.4 
102.5 

:I02.  6 
102.7 

102.  9 

127-9 
128.0 
128.1 

128.3 
128.4 
128.5 
128.6 

153-5 
153-6 
153-8 

153-9 
154-  i 
•154-2 
154-4 

179.0 
179.2 
179-4 

179-6 
179-7 
179-9 
180.  i 

204.8 

205.  2 
205.4 

205.  6 

205.8 

230.4 
230.6 

230.9 
23  •  i 
23  -3 
23  -5 

28  .6 
28  .9 

28  :4 
28.7 
283.0 

•24 
25 

26" 
27 
38 
29 

3' 
32 
33 
34 
35 

25-78 
25.  80 
25-83 
25-85 
25  88 

51-55 
51-60 
5'-65 
-51.70 

77-33 
77-41 
77.48 
77-56 

103.1 

103.3 
103.4 

128.9 
129.0 
129.1 
"29-3 

'  '54-7 
154-8 
"55-0 
155-1 

180.4 
180.6 
180.8 

206.2 
206.4 
206.6 
206.8 

23  .0 
23  -2 
23  -4 
23  -7 

283.6 
283.8 
284.1 
284.4 

3" 
32 
33 
34 

36 
37 
38 

25-90 
25-93 

51-80 
51-85 

77-70 
77-78 

103.6 

\ll:l 

129-5 
129.6 

155-4 
155-6 

i  -3 
i  -5 

207.  2 
207.4 

233-1 
233-3 

284.9 
285.2 

36 
* 

39 
40 

25.98 

51-95 

77-93 

103. 

129.9 

>55-9 

i  .  8 

207.  8 

233-  8 

285.7 

39 

4> 

4- 

26.02 

52-05 

78.08 

104. 

130-2 

156-2 

1  .  2 

208.  2 

234-3 

286.3 

4« 

43 
44 
45 

46 

47 
48 
49 
50 

5" 

52 
53 
54 
55 

56 

26.08 
26.  10 
26.12 

26.15 
26.18 

26.  20 
26.22 
26.  25 

26.  27 
26.  30 
26.32 
26.35 

26.  37 

52.  15 

52.  20 
52.25 

52.30 
52-35 
52.40 
52.45 
52.50 

52.55 
52.60 
52-65 
52.70 
52-74 

78.23 
78.3° 
78.38 

78.45 
78.52 
78.60 
78.67 
78-75 

78.82 
78.90 
78.97 
79.04 
79.12 

104. 
104. 
104. 

104. 

104. 
104. 
104. 
105. 

105. 
105. 
105. 
105. 
105. 

130.4 
130.5 
130-6 

130-8 
130.9 
13  -o 
13  -i 

13  -2 

13  -4 
13  -5 
13  -6 
'3  -7 
13  -9 

156.4 
156.6 
156.8 

156.9 
157-0 
157-2 
157-3 
157-5 

'57-6 
"57-8 
157-9 
158-1 
158.2 

182.5 
,82.7 
182.9 

183.0 
183.2 
183-4 
183.6 
183-7 

183-9 
184.1 
184-3 
184.4 
184.6 

208.6 
208.8 
209.0 

209.2 
209.4 
209.6 
209.8 
2   0.0 

0.  2 
0-4 

0.8 

1.0 

234-7 
234-9 
235-1 

235-4 
235-6 
235-8 
236.0 
236.2 

236.5 
236-  7 
236-9 
237-1 
237-4 

286.8 
287.1 
287.4 

287.6 
287.9 

288.  2 
288.5 
288.7 

289.0 
289.3 
289.6 
289.8 
290.1 

43 
44 
45 

46 
47 
48 
49 
50 

51 

52 
53 
54 
55 

57 
58 
59 

26.42 
26.45 
26.47 

52.84 
52.89 
52-94 

79.27 

79-34 
79.42 

105.7 

105.8 

105.9 

132.1 
132.2 
132-4 

158-5 
158.7 
158.8 

185.0 
.85.1 
185-3 

211.4 

211.  6 
211.8 

237-8 
238.0 
238.2 

2.90.6 
290.9 
291.2 

57 
58 
59 

Horz. 
Dist. 

92.86 

185-7 

278.6 

371.4 

464-3 

557 

650 

743 

836 

1022 

Dist.' 

Hor.  dist.  is  for  30'  point.     Add  or  subtract  .150  ft.  to  each   100    ft.  of 
distance  for  each  10'  departure. 


88 


TOPOGRAPHIC  STADIA   SURVEYING 


TABLE  7 — Continued 

DIFFERENCES   IN   ELEVATION 
16° 


t 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1100 

1 

o 

26.  50 

52-  99 

79-  45 

106.  o 

185  5 

26.  52 

53-04 

79-56 

106.  I 

32'  6 

'59-  i 

185.6 

212.  2 

238.7 

291.7 

2 

26.55 

53-09 

79.64 

106.2 

32-7 

'59-3 

185.8 

212.4 

238-9 

292.0 

3 

26.57 
26.  60 

53-14 

79-71 
79-  78 

106.3 
106.  4 

32-8 

'59-4 

186.0 

212.6 

239-  i 

292.3 

5 

26.62 

53-24 

79-86 

106.5 

33-  l 

'59-7 

186.3 

213.0 

239-6 

292.  5 
292.8 

6 

26.64 

53-29 

79-90 

106.6 

33-2 

'59-9 

186.5 

213-2 

239-8 

293-1 

6 

7 

26.67 

53-34 

80.01 

106.7 

33-3 

160.0 

186.7 

213-4 

240.0 

293-4 

7 

8 

26.69 

53-39 

80.08 

106.8 

33-5 

160.2 

186.8 

213-5 

240.  2 

293-6 

8 

9 

10 

26.  72 
26.74 

53-44 
53.48 

80.15 
8o.,23 

106.  9 
107.0 

33-6 
33-7 

160.3 
160.4 

187.0 
187.2 

213-7 
213-9 

240.5 
240.7 

293-9 
294.2 

9 
10 

II 

26.77 

53-53 

80.30 

107.  I 

33-8 

160.6 

187.4 

214.  I 

240.9 

294.4 

•ii 

12 

26.79 

53.58 

80.38 

107.2 

34-0 

160.8 

187.  5 

24-3 

241.1 

294-7 

•3 

26.82 

53-63 

80.45 

>07-  3 

34-  i 

160.  9 

187.7 

214-5 

24I-3 

295.0 

13 

«4 

26.84 

53-68 

80.52 

107.4 

34-2 

16  .0 

187.9 

214.  7 

24,.6 

295-2 

>4 

15 

26.86 

53-73 

80.60 

107-5 

34-3 

16  .2 

188.  i 

214.9 

241.8 

295-5 

«5 

16 

26.89 

53-78 

80.67 

107.  6 

34-4 

16  .3 

188.2 

215.  i 

242.0 

295-8 

16 

17 

26.  91 

53-83 

80.74 

107.  7 

34-6 

16  .5 

188.4 

215-3 

242.2 

296.0 

17 

18 

26.94 

53-88 

80.82 

107.  8 

34-7 

16  .6 

188.6 

215.5 

242.4 

296.3 

18 

19 

26.96 

53-93 

80.89 

107.8 

34-8 

16  .8 

188.7 

215  7 

242.7 

296.6 

19 

JO 

26.99 

53-98 

80.96 

108.0 

34-9 

16  .9 

188.9 

215-9 

242.9 

296-9 

20 

Ji 

27.01 

54-02 

•04 

108.0 

35-  i 

162.  I 

189.  I 

216.  i 

243-  I 

297-1 

21 

22 

27.04 

54-  07 

.  ii 

08.2 

35-2 

162.2 

189-3 

216.3 

243-3 

297-4 

22 

23 

27.06 

54-  '2 

.  18 

108.2 

35-3 

162.4 

189.4 

216.5 

243-6 

297-7 

23 

24 

27.09 

54-  '7 

.26 

08.3 

35-4 

162.  5 

189.6 

216.  7 

243.8 

297.9 

24 

25 

27.  ii 

54-22 

•33 

108.4 

35-6 

162.7 

189.8 

216.9 

244-0 

298.2 

25 

26 
37 

27-  »3 

27.  16 

54  26 
54-  32 

.40 

•  48 

108.5 
108  6 

35-6 
35-  8 

162.8 
163.  o 

189.9 

217.0 

244.2 

298.4 

26 
27 

28 

27.  1  8 

54-37 

•55 

08.7 

35-9 

163.1 

190.3 

217-5 

244.6 

299.0 

28 

29 

27.  21 

54-4" 

.62 

108.8 

36.0 

163.  2 

190.4 

217-7 

244.9 

299.3 

29 

30 

27-23 

54  46 

•  70 

108.9 

36.2 

if)      1 

163.4 
iftl     C 

190.6 
ton  K 

217.9 

245-  1 

299.6 

-30 

31 
32 
33 

27.28 
27.  30 

54'  56 
54  6  1 
54-  66 

^84 
.92 

109.  I 
109.2 

3°-  3 

36.4 
36.5 

IO3-  5 

163.7 
•63.8 

190.  o 
19  .0 
19  .1 

218.2 
218.4 

245-5 
245-8 

3°o.  i 
300.4 

32 
33 

34 
35 

•if, 

27.35 
27.  38 

54-71 

54-  76 

.10 

109.  3 
109.4 

3^8 

lt\    0 

164.1 

*f*A      1 

19  -5 

218.8 

246.2 

300.9 

35 
76 

3° 
37 
38 

27.40 
27-43 

54-  80 
54-85 

•  '3 

.  21 
.28 

109.  5 
109.6 
109.7 

3".  9 
37-0 
37-' 

104.  3 

164.4 

164.  6 

!!:• 

192.0 

219.2 
19.4 

246.6 
246.8 

3O1-  2 
301.4 
301.7 

3° 
11 

39 

27-45 

54-90 

•35 

109.8 

37-3 

164.7 

192.2 

19.6 

247-1 

302.0 

39 

40 

27.48 

54-95 

2-43 

109.9 

37-4 

164.8 

192.3 

19.8 

247-3 

302.  2 

40 

41 

27-50 

55-00 

82.50 

I        0 

37-5 

165.0 

192.5 

20.0 

247-5 

302.5 

41 

42 

27-52 

55-05 

82-57 

i       i 

37-6 

165.1 

192.7 

20.  2 

247-7 

302.8 

42 

43 

27-55 

55-  'o 

82.60 

I         2 

37-7 

165.3 

192.8 

20.4 

247-9 

303.0 

43 

44 

45 

27-  57 
27.60 

55-  '4 
55-  '9 

82.  72 
82.79 

I       3 
i       4 

37-9 
38-0 

165.  4 

165.6 

193-2 

220.  8 

248.4 

303.3 
303.6 

44 
45 

46 

27.62 

55-24 

82.86 

i       5 

38.1 

165.7 

193-4 

221.0 

248.6 

303.8 

46 

47 

27-  65 

55-29 

82.94 

38-2 

165.9 

193-5 

221.  2 

248.8 

304.  1 

47 

48 

27.67 

55-34 

83.01 

1       7 

38-4 

1  66.  0 

193-7 

221.4 

249.0 

304  4 

48 

49 

27-69 

55-39 

83.08 

i       8 

38-5 

166.2 

193-9 

221.6 

249.  2 

304.  6 

49 

50 

27-72 

55-44 

83-15 

i       9 

38.6 

166.3 

194-0 

221.7 

249-5 

304-  9 

50 

51 

27-74 

55-48 

83-23 

I         O 

38.7 

166.4 

194.2 

221.9 

249-7 

305-2 

5' 

52 

27-77 

55-53 

83-30 

i       i 

38-8 

166.6 

194.4 

222.  I 

249.9 

305-4 

52 

S3 

27.79 

55-58 

83-37 

I         2 

39-0 

166.7 

194.5 

222.3 

250.  I 

305.7 

53 

54 

27.82 

55-63 

83-44 

i       3 

39-  i 

166.9 

194.7 

222.5 

250.3 

306.0 

54 

55 

27-84 

55-68 

83-52 

i       4 

39-2 

167.0 

194.9 

222.7 

250.6 

306.2 

55 

5« 

Z7-86 

55-73 

83-59 

I       4 

39-3 

167.2 

195-0 

222.9 

250.8 

306.5 

56 

57 

27-89 

55-78 

83.66 

i       6 

39-4 

167-3 

195-2 

223-1 

251.0 

306.8 

57 

58 

27.91 

55-82 

83-74 

i       6 

39-6 

.67-5 

195-4 

223-3 

251.2 

307.0 

58 

59 

27.04 

-55-  87 

83-8, 

i       7 

•39-7 

167.6 

195.6 

223-5 

25I-4 

307.3 

59 

Horz. 
Dist. 

91-93 

183-9 

275-  8' 

367-7 

459-7 

552 

644 

735 

827 

ion 

Horz. 
Dist. 

Hor.  rtist.  is  for  30'  point.     Add  or  subtract  .158  ft.  to  each    100  ft.   of 
distance  for  each  10'  departure. 


TOPOGRAPHIC  STADIA  SURVEYING 


89 


TABLE  7 — Continued 

DIFFERENCES    IN    ELEVATION 
17°  to  23° 


t 

17° 

;s° 

19° 

20° 

21° 

22° 

23° 

;  t 

o 

27.  96 

29-39 

30.78 

32.  14 

33-46 

34-73 

35-97 

o 

I 

27-99 

29.42 

30.81 

32.16 

33-48 

34-75 

35-99 

1 

a 

28.  01 

29-44 

30.83 

32.18 

33-50 

34-77 

36.01 

X 

3 

28.04 

29.47 

30.85 

32.21 

33-52 

34-80 

36.03 

S 

4 

28.06 

29.49 

30.87 

32.23 

33-54 

34-82 

36-05 

* 

5 

28.08 

29-51 

30.90 

32.25 

33  57 

34.84 

36.07 

5 

6 

28.  10 

29-53 

30.  92 

32-27 

33.,'59 

34-86 

36.09 

6 

7 

28.13 

29.56 

30.94 

32.30 

33;  6l 

34-88 

36.11 

7 

8 

28.15 

29-58 

30.97 

32.32 

33-63 

34.90 

36.  13 

8 

9 

28.  18 

.  29.  60 

30.99 

32-34 

33-65 

34-92 

36.  15 

9 

10 

28.  20 

29.62 

31-01 

32.36 

3,3-67 

34-94 

36-  17 

IO 

ii 

'28.22 

29-65 

31-04 

;  32.  39 

33-70 

34-96 

36-  '9 

It 

12 

28.25 

29.  67 

31-06 

32.41 

33-72 

34-98 

36.21 

12 

'3 

28.  27 

29.69 

3«-o8 

32.43 

,33-74 

35-oo 

36-23 

13 

«4 

28.30 

29.72 

31.  10 

32.45 

33-76 

35-02 

36-25 

I* 

«5 

28.32 

29-74 

3i-  '3 

32-47 

33.78 

35-  05 

36-27 

15 

16 

28.34 

29.  76 

31-15 

32.49 

33.8o 

35-07 

36.29 

16 

•7 

28.  37 

29.79 

3  -*7 

32.51 

33-82 

35  09 

36.31 

17 

18 

'28.39 

29.81 

3  -19 

32.54 

33-84 

35-  ii 

36.33 

18 

>9 

28.42 

29-83 

3   -22 

32-56 

33-87 

35-13 

36-35 

•9 

20 

28.44 

29.86 

3  -24 

32-58 

33-89 

35  15 

36.37 

20 

21 

28.47 

29.88 

3  -26 

32.  61 

33-91 

35-  17 

36.39 

21 

22 

28.49 

29.90 

3  -28 

32.63 

33-93 

35-19 

36-41 

22 

23 

28.51 

29-93 

3'-3o 

32.65 

33-95 

35-21 

36.43 

23 

24 

28.54 

29-95 

31-33 

32.67 

33-97 

35-23 

36.45 

24 

35 

28.56 

29  97 

31-35 

32.70 

33-99 

35-25 

36.47 

25 

26 

28.58 

30.00 

3'-38 

32.72 

34-oi 

35-27 

36.49 

26 

37 

28.61 

30.02 

3'-40 

32.74 

34-04 

.35-  29 

36.51 

27 

28 

•    28.63 

30.04 

3"-42 

32-76 

34.06 

35-31 

36.53 

28 

29 

28.66 

30.07 

3'-  43 

32-78 

34.08 

35-34 

36.55 

29 

30 

28.68 

30.  09 

3'-47 

32.80 

34-  10 

35-36 

36  57 

jo 

31 

28.70 

30.  n 

31-49 

32-83 

34-  12 

35  38 

36.59 

31 

32 

28.73 

30-  '4 

3  -51 

32.85 

34-  14 

35-40 

36.61 

32 

33 

28.75 

30.16 

31-54 

32.87 

34-16 

35-42 

36.63 

33 

34 

28.77 

3°-  1  9 

3  -56 

32.89 

34-  1  8 

35-44 

36.65 

34 

35 

28.80 

30.21 

31-58 

32-91 

34-21 

35  46 

36.67 

35 

36 

28.82 

00-23 

3  -60 

32-93 

34-23 

35-48 

36.69 

36 

37 

28.85 

30.  26 

31-63 

32.96 

34-25 

35-50 

36.71 

37 

38 

28.87 

30.  28 

31-65 

32.98 

34-  27 

35-52 

36.73 

3* 

39 

28.89 

30.30 

31-67 

33-oo 

34-29 

35-54 

36.75 

39 

40 

28.92 

30.32 

31.69 

33-02 

34  3i 

35.56 

36.77 

40 

41 

28.94 

30.36 

31-72 

33-05 

34-33 

35-58 

36.79 

4» 

42 

28.96 

30.37 

31-74 

33-07 

34-35 

35-6o 

36.80 

42 

43 

28.99 

30.39 

31-76 

33-09 

34-38 

35-62 

36.82 

43 

44 

29.01 

30.41 

3'-78 

33   1  1 

34.40 

35  64 

36.84 

44 

45 

29-04 

30-44 

33-  13 

34-42 

35-66 

36.86 

45 

46 

29.06 

30.46 

31-83 

33-  1  5 

34-44 

35-68 

36.88 

46 

47 

29.08 

30-49 

31-85 

33-18 

34.46 

35-70 

36.  90 

47 

48 

29.  ii 

30.5> 

31-87 

33-20 

34-48 

35-72 

36.92 

48 

49 

=9-  '3 

30.53 

3  -90 

33-32 

34-50 

35-74 

36.94 

49 

50 

29-  '5 

30.55 

31-92 

33-24 

34-52 

35.76 

36.96 

50 

S" 

29.  1  8 

30.58 

31-94 

33-26 

34-54 

35-78 

36.98 

5» 

52 

29.20 

30.  60 

3L96 

33,  28 

34-57 

35-80 

37.00 

52 

53 

29-23 

30.62 

3'-99 

33-31 

34  59 

35-83 

37-02 

53 

54 

29.25 

30-65 

32.01 

33-33 

34-61 

35-85 

37-04 

54 

55 

29-27 

30.67 

32-03 

33-  35 

34-63 

35-87 

37-o6 

55 

56 

29.30 

30.69 

32-05 

33-37 

34.65 

35.89 

37-oS 

S& 

57 

29.32 

30.72 

32.07 

33  39 

34.67 

35-91 

37-1° 

57 

58 

29-34 

30.74 

32.09 

33-41 

34.69 

35-93 

37-12 

5* 

59 

29-37 

30.76 

32-12 

33-44 

34.71 

35-95 

37-14 

59 

Horz. 

90.96 

89-93 

88.86 

87.74 

86-57 

85-36 

84-10 

Hon. 

Dist. 

Dist. 

Horz. 
Corr. 

'67 

3 

.182 

.191 

.198 

.206    1 

3 

Horz. 
Con. 

90 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  7 — Concluded 

DIFFERENCES   IN   ELEVATION 
34°  to  29° 


* 

24° 

25° 

26* 

27° 

28° 

29", 

•'. 

o 

37-16 

38.30 

39-49 

4°-45 

41-45 

42.40 

0 

1 

37.18 

38-32 

39-42 

40.47 

4'-47 

42.42 

i 

2 

^57-20 

.38.34 

39-44 

40.  49 

41.48 

42-43 

i 

3 

37-  22 

38-36 

39-46 

40.  5' 

4'-  50 

42-45 

3 

4 

37-23 

38-38 

39-47 

40-52 

4  -52 

42.46 

4 

5 

37-25 

38.40 

39-49 

40-54 

4'  -54 

42.48 

5 

6 

37-27 

38.41 

39-51 

40-55 

41-55 

42-49 

6 

7 

37-29 

38.43 

39-5' 

40-57 

4>-57 

42-5" 

7 

8 

37.31 

38.45 

39-55 

40.59 

41.58 

42-53 

8 

9 

37-33 

38.47 

39-56 

40.  6  1 

41.60 

42.54 

9* 

10 

37-35 

38.49 

40.  62 

41.61 

42.56 

10 

,, 

37-37 

38.52 

39.60 

40.64 

41.63 

42.58 

it 

12 

37-39 

38.53 

39-61 

40.66 

41-65 

42-59 

12. 

13 

37-41 

38.55 

'  39-  63 

40.68 

41.67 

42.  60 

1J 

M- 

37-43 

38-56 

•39-65 

40.69 

41.68 

42.62 

I* 

15 

37-45 

35-58 

39-67 

40.71 

41.70 

42.64 

15 

16 

37-  47 

38  Bo 

39-69 

40.72 

41.71 

42-65 

16 

17 

37-49 

38^62 

39-7' 

40.  74 

4'-73 

42.66 

17 

18 

37-  5  « 

•38.  64 

39-72 

40.76 

41-74 

42.68 

IS 

'9 

37-53 

38.66 

39-74 

40.78 

41.76 

42.70 

'9 

30 

37-54 

.38-67 

39-  76 

40.  79 

41-77 

42.71 

20 

21 

37-56 

.38.69 

39-78 

40.  8  1 

41-79 

42.72 

2, 

22 

39-79 

40.82 

41.8! 

42-74 

22 

23 

37.60 

38.73 

39-82 

40.84 

41.83 

42-76 

23 

24 

37-62 

38.75 

39-83 

40.86 

1.84 

42-77 

24. 

25 

37-64 

38.76 

39-85 

40.88 

1.86 

42.78 

25 

26 

37-66 

38.78 

*39-  86 

40.89 

1.87 

42.  80 

26 

27 

37-68 

38.80 

39-88 

40.91 

1.89 

42.82 

27 

28 

37-70 

38.82 

39-90 

40.92 

1.90 

42.83 

28 

29 

37-72 

38.84 

39-92 

20.  94 

41.92 

2.85 

29 

30 

37-74 

38..S6 

39-93 

40.96 

41  93 

2.86 

30 

31 

37-76 

38.88 

39-95 

40.98 

41-95 

2.88 

3» 

32 

37-77 

38.89 

39-97 

40.99 

41-97 

2.89 

32 

33 

37-79 

38-9' 

39-99 

.01 

41.99 

2.91 

33- 

34 

37-8i 

38.93 

40.  oo 

.  02 

2.00 

2.92 

34 

35 

37-83 

40.02 

.04 

2.02 

2.94 

35 

36 

37.85 

38.97 

40.04 

.06 

2.03 

2-95 

36 

37 

37-87 

38.99 

40.06 

.08 

2.05 

2.97 

37 

38 

37-89 

39.00 

40.07 

.09 

2.06 

2.98 

3» 

39 

37-9' 

39-02 

40.09 

.  1  1 

2.08 

43.00 

39 

40 

37-93 

39-04 

40.11 

.  12 

42.09 

43-01 

40 

41 
42 
43 

37-95 
37-  96 
37-98 

39-  06 
39.08 
39-  >o 

40.14 
40.  1  6 

.16 

42.  4 

43-04 
43.06 

4* 
43 

44 

38.00 

39-" 

40.18 

•>9 

2-  5 

43-07 

44 
45 

45 

46 

38.  02 
38.04 

39-  '5 

40.21 

.22 

2.19 

43-  '0- 
43-  12 

46 
47 

48 

38.08 

39-  "8 

40.24 

.26 

2.22 

43-  >3 

49 

38.  10 

39-20 

40.26 

.28 

2.  24 

43-  "5 

49 

50 

38... 

39-2? 

40.28 

•29 

42.25 

43-16 

50 

5« 

38.13 

39-24 

40.30 

•31 

42.  26 

43-'7 

5« 

52 

38.15 

39-26 

40.31 

•32 

42.28 

43.18 

5» 

53 

38.17 

39-27 

40-33 

•34 

42.30 

43-20 

53 

54 

38-19 

39-29 

40.35 

•35 

42.  31 

43-21 

54 

55 

.  38-21 

39-31 

40.37 

•37 

42-33 

43-23 

55 

56 
57 

38-23 

38.25 

39-33 
39-  35. 

40.38 
40.40 

•39 
.41 

42.34 
42.36 

43-24 
43-26 

56 

57 

58 

38.26 

39;.36 

40.42 

.42 

42.37 

43-27 

58 

59 

38.28 

40.44 

•  43 

42.39 

43-29 

59 

'Horz. 
Dist, 

82.80 

8I-.47 

80.09 

78.68 

.77-23 

75-75 

Horz. 
Dist. 

Horz. 
Corr. 

.219 

.226 

•233 

.238 

.344 

.250 

Horz., 
Corr; 

TOPOGRAPHIC   STADIA   SURVEYING  91 

Conversion  of  Feet  to  Decimals  of  a  Mile. 

Table  8  is  a  table  for  the  conversion  of  feet  to  decimals  of  a 
mile.  A  table  of  this  character  will  be  found  convenient 
when  the  mile  is  the  unit  for  platting.  This  table  is  repro- 
duced by  permission  from  publications  of  the  U.  S.  Geological 
Survey. 

For  any  distance  expressed  in  feet  which  is  likely  to  come 
into  consideration  in  making  a  stadia  survey  the  equivalent 
fraction  of  a  mile  is  noted. 


92 


TOPOGRAPHIC  STADIA  SURVEYING 


TABLE  8 
CONVERSION  OP  FEET  TO  DECIMALS  OP  A  MILE 

(By  permission  of  the  U.  S.  Geological  Survey) 


Feet. 

Mile. 

Feet. 

Mile. 

Feet. 

Mile. 

Feet. 

Mile 

Feet. 

Mile. 

Feet. 

Mile. 

Feet. 

Mile. 

100 

0.019 

600 

0.114 

1  100 

o.  208 

1600 

0.303 

2100 

0-398 

2600 

0.492 

3100 

•0.587 

10 

.021 

10 

.  116 

10 

.  210 

10 

•305 

10 

.400 

10 

•494 

•  589 

20 

.023 

20 

.118 

20 

.  212 

20 

•  3°7 

20 

.402 

20 

.496 

20 

•59" 

30 

.025 

30 

.  120 

3«> 

.214 

3° 

.309 

30 

•  404 

30 

.498 

30 

•593 

4O 

.026 

40 

.  122 

40 

.216 

40 

•3" 

40 

•  405 

40 

•  500 

40 

•595 

SO 

.028 

50 

•  '24 

50 

.218 

5° 

•3'3 

50 

.407 

50 

•  502 

50 

•596 

60 

.030 

60 

•'25 

60 

.219 

60 

•  3"4 

60 

.409 

60 

•5°4 

60 

•598 

70 

.032 

70 

.127 

70 

.  221 

70 

•  3'6 

70 

.411 

70 

•  506 

70 

.600 

So 

•O34 

80 

.129 

So 

.223 

80 

.318 

80 

•4'3 

So 

•  508 

80 

.602 

90 

.036 

90 

.I3« 

90 

.225 

90 

.320 

90 

•4'5 

90 

•509 

90 

.604 

200 

.038 

700 

•133 

1  200 

.227 

1700 

.322 

22OO 

.417 

2700 

••5>i 

3200 

10 

.606 
.  608 

20 

.  040 

.042 

20 

.136 

20 

•23' 

20 

.326 

20 

.420 

20 

•515 

.610 

30 

.044 

3° 

.138 

30 

•233 

30 

.328 

30 

.422 

30 

•5'7 

30 

.612 

40 

.046 

40 

.140 

40 

•235 

40 

••330 

40 

.424 

40 

•519 

40 

.614 

50 

•  °47 

SO 

.142 

50 

.236 

50 

•33' 

5° 

.426 

50 

•521 

50 

.616 

60 

.049 

60 

.144 

60 

-238 

60 

•333 

60 

.428 

60 

•523 

60 

.617 

70 

.051 

70 

.146 

70 

.240 

70 

•335 

70 

•43° 

70 

•525 

70 

.619 

80 

•053 

80 

.148 

So 

.242 

80 

•337 

80 

•432 

80 

•527 

So 

.  621 

90 

•055 

90 

.150 

90 

.244 

90 

•339 

90 

•434 

90 

•529 

90 

-623 

300 

•057 

800 

•  152 

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CHAPTER  IX 
HOW  TO  USE  THE  STADIA  DIAGRAM 

Formulas  and  the  Diagram.  The  diagram  for  the  reduc- 
tion of  stadia  notes  which  accompanies  this  manual,  is  pre- 
pared specifically  as  a  graphic  solution  at  one  operation  of 
the  approximation  formulas: 

Z)  =  (r+e)  cos2  «;         (27) 

and 

h  =  (r  +e)  sin  a  cos  a (28) 

But  the  diagram  may  also  be  used  in  ascertaining  the  values 
of  r  cos2  a  and  r  sin  a  cos  a  in  the  correct  formulas  (Eq.  17) 
and  (18)  and  for  the  approximation  of  (r+1)  cos2  a  and  (r  +  1) 
sin  a  cos  a  in  formulas  (29)  and  (30).  As  the  formulas  (17) 
and  (18)  need  only  be  used  for  sights  to  turning  points  and 
on  surveys  requiring  more  than  ordinary  precision,  it  would 
seem  advisable  to  give  preference  to  reduction  tables  when- 
ever such  approximation  formulas  as  (27)  and  (28),  or  (29) 
and  (30)  will  not  serve. 

To  Use  the  Diagram:  Follow  the  angle  ray  which  corre- 
sponds to  the  angle  a  of  elevation  or  depression,  to  its  inter- 
section with  the  curved  line  which  corresponds  to  the  value 
(r+e)  in  formulas  (27)  and  (28).  Holding  a  needle  point 
at  the  intersection  thus  determined  read  off  by  the  aid  of 
the  vertical  lines  the  horizontal  distance  D,  that  is  (r  -\-e)  cos2  a. 
and  by  the  aid  of  the  horizontal  lines  the  difference  in  eleva- 
tion h,  that  is  (r+e)  sin  a  cos  a. 

Or  make  the  more  convenient  determination  sufficiently 


94  TOPOGRAPHIC  STADIA  SURVEYING 

close  in  all  ordinary  cases,  by  entering  the  diagram  with 
(r+1)  instead  of  (r+e). 

Whenever  the  use  of  the  approximation  formulse  are  per- 
missible, as  in  the  determination  of  topography,  the  diagram 
gives,  at  once,  the  distance  and  the  difference  in  elevation, 
for  any  rod-readings  and  any  vertical  angles  within  their 
scope.  Distance  should  be  read  to  the  nearest  foot  and  differ- 
ence in  elevation  to  the  nearest  tenth  of  a  foot. 

When  points  are  located  by  the  intersection  of  sights  from 
two  instrument  stations,  the  horizontal  distances  from  each 
of  these  two  stations  are  scaled  from  the  map.  The  diagram 
js  now  entered  with  each  of  these  distances  and  needle  points 
are  placed  at  the  intersections  of  these  distances  with  the 
corresponding  angle  rays  of  the  measured  angles  of  elevation 
or  depression.  If  the  same  difference  in  elevation  is  not 
indicated  by  both  needle  points  the  mean  value  should  be 
jecorded. 

The  author,  early  in  his  experience  on  topographic  surveys, 
constructed  a  diagram  as  here  described  based  on  the  funda- 
mental approximation  formulse  (27)  and  (28)  and  has  found 
the  same  a  great  convenience,  fulfilling  every  requirement 
both  as  to  minimizing  mental  effort,  reducing  the  chance  of 
error  and  insuring  accuracy  of  results.  It  eliminates  the 
undesirable  features  of  many  of  the  other  diagrams  at  various 
times  suggested  for  use,  which  do  not  give  final  results  with- 
out additions  or  subtractions. 

The  explanatory  notes  for  the  use  of  the  diagram  are  as 
follows: 


TOPOGRAPHIC  STADIA   SURVEYING  '95 

STADIA  DIAGRAM 

For  Instruments  rated  1  to  100 
Graphical  Solution  of  the  Approximation  Formulas: 

D  =  (r  +e)  cos2  «  f  D  =  (r +1)  cos2  a 

or    \ 
h  =  (r  +e]  sin  a  cos  a         [   h  =  (r+l)  sin  a  cos  a 

Where 

r  =  reading  on   a  vertical  rod. 
a  =  vertical  angle. 
D  =  horizontal  distance. 
h  =  difference  in  elevation. 

e=  instrument   constant   =  the   distance   of  the   outside 
focal  point  of  the  object  lens  from  the  instrument  axis. 

Directions : 

Follow  the  vertical  angle  ray  to  the  curved  line  (r-\-e)  or 
(r +  1),  as  the  case  may  be,  and  read  D  on  the  horizontal  scale 
and  h  on  the  vertical  scale. 

NOTE. — The  diagram  can  also  be  used  to  find  the  value  of 
r  cos2  a  and  of  r  sin  a  cos  a. 


INDEX 


Accuracy  of  stadia  surveys 48 

Alidade,  vertical  angles  measured  with 44 

Anallatic  point,  defined 2 

Anderson's  stadia  reduction  table,  explanation 63 

Approximation  formulas  for  distance  and  difference  in 

elevation 16 

Casgrain,  W.  T.,  and  A.  Noble,  publication  by,  referred  to.  .  27 
Corrections,  tables  of,  for  departure  of  the  stadia  rod  from 

a  true  vertical  position 49,  50 

Corrections,  tables  of,  when  sighting  point  does  not  bisect 

the  intercept 41,  46 

Cross-hairs,  adjustable  or  fixed 1 

Departures  from  ordinary  practice  in  stadia  surveying 30 

Diagrams  for  stadia  reduction 19,  22,  93 

Diagram  furnished  with  manual 22 

Diagrammatic  solution  of  stadia  formulas 19 

Diagram  with  manual,  how  to  use 22,  93 

Error,  due  to  inclined  rod 47 

Error,  when  sighting  point  does  not  bisect  the  intercept. ...  44 

Feet,  conversion  into  miles,  table 91 

Focal  distance,  principal,  defined 3 

Formula,  the  stadia 9 

Formulas,  basic 3 

Formulas  for  inclined  sights 12 

Formulas  for  inclined  sights,  approximation 16 

Formulas,  modification  of,  for  slide-rule  work 24 

Formulas,  use  of 17 

Hall,  Wm.  Hammond,  referred  to 30 

Height  of  telescope  above  station  plug  can  be  eliminated 

from  notes 35 

Inclined  sights,  approximation  formulas 16 

Inclined  sights,  formulas 12 

Instrument  constant 2,  10 

97 


98  INDEX 

PAGE 

Intercept,  defined 2 

Lietz,  A.  Co.,  referred  to . 34 

Lietz,  A.,  paper  on  the  Porro  telescope 6 

Magnetic  needle,  surveys  with  use  of 28,  37 

Magnetic  needle,  surveys  without  use  of 26 

Methods  of  stadia  surveying. 26 

Miles,  conversion  into  feet 91 

Noble,  A.,  and  W.  T.  Casgrain,  publication  by,  referred  to .     27 

Porro  telescope 5 

Porro  telescope,  described  by  A.  Lietz 6 

Rating  factor 10 

Rating  factor,  defined 3 

Rating  factor,  determination  of 10 

Refraction,  the  effect  of 51 

Rod  reading,  defined 2 

Rod,  special  type  of 30 

Rod,  the  target 2 

Rod,  the  telemeter  or  stadia,  defined 2 

Sighting  point,  defined 2 

Slide-rule  as  an  aid  in  reducing  stadia  work 24 

Stadia  formula. 9 

Stadia  formulas,  diagrammatic  solution 19 

Stadia  field  notes 38 

Stadia  field  notes,  sample  pages : . .     40 

Stadia  notes,  the  platting  of 52 

Stadia  reduction  diagrams 19,  22,  93 

Stadia  reduction  diagram,  special  type  of,  how  to  use. ...   22,  93 
Stadia  reduction  table,  Anderson's,  by  permission  of  U.  S. 

Geol.  Survey,  explanation 63 

Stadia  reduction  table,  for  readings  of  100  feet  and  instru- 
ments rated  1  to  100,  explanation  of 55 

Stadia  reduction  with  aid  of  slide-rule 24 

Stadia  rod,  defined 2 

Stadia  surveying,  methods  of 26 

Stadia  surveying,  with  use  of  magnetic  needle 28,  37 

Stadia  surveying,  without  use  of  magnetic  needle 26 

Stadia  surveys,  accuracy  of 48 

Stadia  surveys,  reference  to  Noble  and  Casgrain 27 

Stadia  unit,  defined 3 


INDEX  99 


TABLES 


1.  Corrections  for  too  large  a  vertical  angle 45 

2.  Corrections  for  too  small  a  vertical  angle 46 

3-4.  Corrections  for  departure  of  rod  from  a  true  vertical.  49,  50 

5.  Values  of  e  cos  a.  and  e  sin  a 54 

6.  Stadia  reduction  table  for  a  rod  reading  of  100  ft 55 

7.  Stadia  reduction  table,  U.  S.  Geol.  Survey  (Anderson).  63 

8.  Conversion  of  feet  into  miles 91 

Tachymetry,  defined 1 

Telemeter  constant,  defined 2 

Telemeter,  defined 1 

Telemeter  or  instrument  constant 10 

Telemeter  rod 2 

Telemeter  rod,  special  type  of 30 

Telemeter  surveys,  accuracy  of 48 

U.  S.  Geological  Survey,  reduction  table 63 

Vertical  angles,  measured  with  alidade 44 

Von  Geldern,  Otto,  referred  to 55 


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